Betting teams at shorter odds reduces variance. This seems correct.

Does betting shorter odds reduce Bankroll swings too using the same edge % per bet?

To give you a example using Kelly and a $1000 bank

Betting -500 odds with a 5% edge Kelly says to bet $250

While betting the outsider in the same game at +400 odds with the same 5% edge, Kelly says to bet $13.

If you're betting teams at shorter odds using Kelly, you are outlaying more dollars per game compared to betting longer priced teams where you would be outlaying less per game using the same edge percentage.

I'm assuming for this reason the bankroll will fluctuate more while on a losing run backing shorter odds compared to betting teams at longer odds, or is this thinking wrong?

If you're kelly-betting in both cases then the bankroll swings are the same in theory, because for instance, in both cases there's a 1% chance of being reduced to $10 from your original $1000 (in an infinite timeline).

However, the -500 kelly bet grows your bankroll more quickly, because

(1+.25*.2)^.875 * (1-.25)^.125
>
(1+.0125*4)^.21 * (1-.0125)^.79

I done a quick calculation if I bet -500 odds only with the 5% edge for 19 bets in a row.

After 19 losing bets in a row the Kelly bank will go from $1000 to less than $5.

But after 19 losses betting in a row betting +400 odds only with the same 5% edge, the Kelly bank will go from $1000 to $789.

The bank will go busto a lot quicker betting shorter odds compared to longer odds bets.

Doesn't this suggest bigger bankroll swings betting shorter odds, or am I wrong?

That's not the whole story.
With the -500 bet, the chance of 19 losses in a row is .125^19 = 1 in 1.44 * 10^17
With the +400 bet, the chance is 1 in 88

Thank you.