Is it a trivial matter, or is it more important that we do not give away our strength or weakness, by betting the same size all the time?

What do you prefer and why?

All sizings have their place from 10% pot to 10 times the pot.
There's nothing inherently better about 2/3 or 3/4

wow, that's smth I never thought about

Bet sizing should vary for many reasons, but hand strength should not be one of them (unless you also balance your hand strength with that bet sizing).

2/3 to 3/4 PSB is a pretty standard, neutral bet sizing that does not give away a lot of info, but it is not always the best bet size to use.

Hand strength is definitely one of the main variables for betsizing

Unless you balance your range, coupling hand strength to bet sizing is playing your cards face up.

Now, loosely coupling your hand strength or hand type to your bet sizing is OK

You can vary your bet size based on hand strength, so long as you balance it correctly. It's easy to create tells if you're not careful though.

I like to lump my entire range into one or two strategically distinct sizes at each point in the hand. 75% pot and 66% pot are so similar I would just pick one and stick with it. But feel free to freestyle.

Just elaborating on balance a bit. Caveat: My playing style is a bit antiquated (I don't really know or understand GTO bet sizing).

I usually have small bets(usually near min raise preflop, or 1/4 pot post flop) that I use as either a probe(if I have thin value), a tickler(if I have a monster and want to generate a response), a pot builder(If I have a monster or a nut draw, and want to build the pot), or as a way to try and control the action to see another card cheaply. I have a normal sized (1/2 to full PSB) which I use as a value bet, a bluff, or a semibluff. And I have a defensive bet (>PSB) which I use to protect vulnerable made hands (like TPTK on a wet board), semibluff with a draw, and value bet with a hand.

Each hand has several different bet types I can use, and I try to keep the percentages of bet types I use appropriate to the type of table I am at. And then, to each bet type, I adjust the frequency of each hand type I might use on that action. It comes out to something like saying 'In middle position with a TPTK on a two flushed board, with a a spazzy LAG behind me, 75% I will bet standard, 10% I will check, 10% I will overbet to rep a draw, and 5% I will bet small to generate a bluff'.

So, yes, while hand strength is a major factor in determining how you size your bets, it is not a direct or linear correlation. You still have to include a range in order to disguise your hand strength, or else everyone will start to pick up on 'He always open limps from EP or UTG with AA or KK' or similar bet sizing tells.