I think that the following actions (in the hand histories at the end of this post) should be illegal according to the rules of NLHE:

• In hand #234100640375: nicofellow: raises $10.05 to $11
• In hand #230963774440: Basmatillo: raises $14.13 to $15
• In hand #234890048642: InsideTheBag: raises $8.07 to $8.69

The relevant rules:

• Poker TDA 2019, Rule #47: Re-Opening the Bet.
• Robert's Rules, Section 14: No-Limit Rules: Rule #2, Rule #3, and Rule #4.

PokerStars Hand #234100640375: Hold'em No Limit ($1/$2 USD) - 2022/02/15 16:17:21 ET
Table 'Leonid V' 6-max Seat #6 is the button
Seat 1: nicofellow ($232 in chips)
Seat 2: tphfloripa ($5.45 in chips)
Seat 3: UBERTAKER ($205.55 in chips)
Seat 4: kebab-setä ($241.67 in chips)
Seat 5: Marcoasdf ($441.82 in chips)
Seat 6: RusBigFishKa ($202.77 in chips)
nicofellow: posts small blind $1
tphfloripa: posts big blind $2
*** HOLE CARDS ***
UBERTAKER: raises $2.50 to $4.50
kebab-setä: folds
Marcoasdf: folds
RusBigFishKa: folds
nicofellow: calls $3.50
tphfloripa: calls $2.50
*** FLOP *** [6h Kd Kc]
nicofellow: checks
tphfloripa: bets $0.95 and is all-in
UBERTAKER: calls $0.95
nicofellow: raises $10.05 to $11
UBERTAKER: calls $10.05
*** TURN *** [6h Kd Kc] [Js]
nicofellow: checks
UBERTAKER: bets $11.43
nicofellow: folds
Uncalled bet ($11.43) returned to UBERTAKER
*** RIVER *** [6h Kd Kc Js] [Qh]
*** SHOW DOWN ***
UBERTAKER: shows [6c 6d] (a full house, Sixes full of Kings)
UBERTAKER collected $19.10 from side pot
tphfloripa: shows [Kh 3h] (three of a kind, Kings)
UBERTAKER collected $15.53 from main pot
tphfloripa cashed out the hand for $2.46 | Cash Out Fee $0.02
*** SUMMARY ***
Total pot $36.45 Main pot $15.53. Side pot $19.10. | Rake $1.82
Board [6h Kd Kc Js Qh]
Seat 1: nicofellow (small blind) folded on the Turn
Seat 2: tphfloripa (big blind) showed [Kh 3h] and lost with three of a kind, Kings (cashed out).
Seat 3: UBERTAKER showed [6c 6d] and won ($34.63) with a full house, Sixes full of Kings
Seat 4: kebab-setä folded before Flop (didn't bet)
Seat 5: Marcoasdf folded before Flop (didn't bet)
Seat 6: RusBigFishKa (button) folded before Flop (didn't bet)

PokerStars Hand #230963774440: Hold'em No Limit ($1/$2 USD) - 2021/10/28 19:11:45 ET
Table 'Hubei' 6-max Seat #5 is the button
Seat 1: AWilliamsA ($214.30 in chips)
Seat 2: Basmatillo ($553.66 in chips)
Seat 3: tigermani ($97.40 in chips)
Seat 4: Raven8808 ($5.87 in chips)
Seat 5: geniy2009 ($200 in chips)
Seat 6: Prokravyaka ($200 in chips)
Prokravyaka: posts small blind $1
AWilliamsA: posts big blind $2
*** HOLE CARDS ***
Basmatillo: raises $3 to $5
tigermani: calls $5
Raven8808: calls $5
geniy2009: folds
Prokravyaka: folds
AWilliamsA: folds
*** FLOP *** [2h Jc 4c]
Basmatillo: checks
tigermani: checks
Raven8808: bets $0.87 and is all-in
Basmatillo: raises $14.13 to $15
tigermani: calls $15
*** TURN *** [2h Jc 4c] [3h]
Basmatillo: bets $82
tigermani: calls $77.40 and is all-in
Uncalled bet ($4.60) returned to Basmatillo
*** RIVER *** [2h Jc 4c 3h] [Tc]
*** SHOW DOWN ***
Basmatillo: shows [Kh Ks] (a pair of Kings)
tigermani: shows [6d 5h] (a straight, Deuce to Six)
tigermani collected $181.34 from side pot
Raven8808: shows [Qd 9s] (high card Queen)
tigermani collected $19.58 from main pot
*** SUMMARY ***
Total pot $203.67 Main pot $19.58. Side pot $181.34. | Rake $2.75
Board [2h Jc 4c 3h Tc]
Seat 1: AWilliamsA (big blind) folded before Flop
Seat 2: Basmatillo showed [Kh Ks] and lost with a pair of Kings
Seat 3: tigermani showed [6d 5h] and won ($200.92) with a straight, Deuce to Six
Seat 4: Raven8808 showed [Qd 9s] and lost with high card Queen
Seat 5: geniy2009 (button) folded before Flop (didn't bet)
Seat 6: Prokravyaka (small blind) folded before Flop

PokerStars Hand #234890048642: Hold'em No Limit ($1/$2 USD) - 2022/03/18 22:04:58 ET
Table 'Cohnia II' 6-max Seat #6 is the button
Seat 1: InsideTheBag ($200 in chips)
Seat 2: bigseljak ($92.05 in chips)
Seat 3: kevin78238 ($9.62 in chips)
Seat 4: pokher121278 ($54.32 in chips)
Seat 5: SnoopAly ($225 in chips)
Seat 6: Basmatillo ($218.47 in chips)
InsideTheBag: posts small blind $1
bigseljak: posts big blind $2
*** HOLE CARDS ***
kevin78238: calls $2
pokher121278: folds
SnoopAly: folds
Basmatillo: folds
InsideTheBag: raises $7 to $9
bigseljak: calls $7
kevin78238: calls $7
*** FLOP *** [4h 3d 5h]
InsideTheBag: checks
bigseljak: checks
kevin78238: bets $0.62 and is all-in
InsideTheBag: raises $8.07 to $8.69
bigseljak: folds
Uncalled bet ($8.07) returned to InsideTheBag
*** TURN *** [4h 3d 5h] [5c]
*** RIVER *** [4h 3d 5h 5c] [9s]
*** SHOW DOWN ***
InsideTheBag: shows [As 8d] (a pair of Fives)
kevin78238: shows [Tc Ac] (a pair of Fives - Ace+Ten kicker)
kevin78238 collected $26.83 from pot
*** SUMMARY ***
Total pot $28.24 | Rake $1.41
Board [4h 3d 5h 5c 9s]
Seat 1: InsideTheBag (small blind) showed [As 8d] and lost with a pair of Fives
Seat 2: bigseljak (big blind) folded on the Flop
Seat 3: kevin78238 showed [Tc Ac] and won ($26.83) with a pair of Fives
Seat 4: pokher121278 folded before Flop (didn't bet)
Seat 5: SnoopAly folded before Flop (didn't bet)
Seat 6: Basmatillo (button) folded before Flop (didn't bet)

Lol.

I assume that the Poker TDA Rules and the Robert's Rules of Poker represent what I think of as the "standard" rules of poker.

I concede that casinos (whether live or online) are not required use these standard rules of poker in their games. But in my opinion, if a casino deviates from the standard rules, then these "house rules" should be explained somewhere on their website's help pages.

The PokerStars website help pages contain an article titled "Poker rules for side pots and betting" that has a subsection titled "No-Limit cannot re-raise small all-in Bet", which explains that PokerStars does in fact follow the "standard" rules in this case at least. This is what it says under that subsection:
The most crucial part of that article is the following:
"A player who has already acted and is not facing a full-size wager may not subsequently raise an all-in bet that is less than the minimum bet or less than the full size of the last bet or raise."

Here' how I understand that sentence:
"A player who has already acted" means a player who has either checked, called, bet, or raised on the current street.
"[A player who] is not facing a full-size wager" means that the amount of money the player would have to put into the pot in order to call is less than either the minimum bet or the last bet/raise (whichever is larger).
"Minimum bet" is defined in Robert's Rules of Poker, Section 14, Rule #2 as equal to the size of the big blind (barring any house rules).

For example, in the PokerStars Hand #234100640375, when nicofellow raises $10.05 to $11 on the flop, at that point he has already acted (checked) on the current street (flop), and the amount he would have to call ($0.95) is less than the minimum bet ($2). Therefore he should not be allowed to make that raise (according to the rules explained in the PokerStars help pages).

That should have said:
...the amount of money the player would have to put into the pot in order to call is less than either the minimum bet or the last full bet/raise on the current street (whichever is larger).

It's been a while but I'm still hoping that someone (with knowledge) would confirm whether or not my interpretation of the rules is correct.

I found what I'd consider proof that my interpretation of the rules is correct. Sadly, it's in a discussion forum post instead of some official poker rules but I trust it because it's a PokerTDA discussion forum.

The question (paraphrased):
NLHE
Blinds 500-1000
Three players on the turn
Player A: Check
Player B: Check
Player C: All-in for 600

Does the short all-in reopen the betting to the players A and B?

The answer (paraphrased):
No. Players A and B may fold or call the action only 600. The reason is, the 600 is less than the 1000 minimum required to reopen the betting.

That example is essentially what happens (on the flop) in all three hand histories I posted.

And given what the PokerStars support documentation says under Poker rules for side pots and betting: No-Limit cannot re-raise small all-in Bet, this is definitely a bug as opposed to an intentional house rule.

I tried sending a bug report about this to PokerStars using their contact form but because I don't have a PokerStars account, I received an automated email reply that said:
The email address you're using isn't registered to any account. We need to review your account to help you.

Which basically means they didn't get my bug report, I think. In case anyone would like to inform them about this issue for me, the following is the bug report I tried to send them:

While performing statistical analysis of hand histories from PokerStars (among others), I detected some hands that broke the game logic model I had programmed in my hand history parser. The reason was that in these particular hands, a player raised in a game state where a raise was (supposed to be) illegal. Here's a summary of the problem:

In a game of No-Limit Hold'em, where big blind is equal to $1000, the flop is reached by three active players, and the following actions occur:
Player A: checks
Player B: checks
Player C: bets $600 and is all-in

It's now player A's turn to act, and he shouldn't be able to raise because player A has already acted and is now facing a bet of $600 which is less than the $1000 minimum (the amount of the big blind) required to reopen the betting. There is an informative discussion about this exact matter on the following PokerTDA discussion thread, which contains lots of informative details:
https://www.pokertda.com/forum/index.php?topic=663.0

The aforementioned hand histories I detected can be identified by the following numbers (which I'm sure you can find in your databases):
#229344212256
#230963774440
#234100640375
#234890048642