Deductions & credits

That $500 was not a contribution to the HSA for 2021. 

"I just want to know that we're paying the taxes on that excess $500. Maybe that was resolved in 2021 since he withdrew the excess $500 before we filed our return? "

You don't need to pay any taxes on that $500, because it was a personal contribution, not through his employer. When there is an "employer" contribution (that is, an amount with code W in box 12 on your W-2), this the code W amount is removed from Wages in boxes 1,3, and 5, making the HSA employer contributions not taxed. So when the excess is from the employer contributions, the excess is added back to line 8 as Other Income, because it had mistakenly been removed from income before the W-2 was printed.

However, a personal or direct contribution doesn't do this since it does not go through the W-2. Instead, the direct HSA contribution appears on line 13 of Schedule 1 (1040). So if some of that direct HSA contribution is excess, TurboTax just subtracts that from the amount it was going to put on line 13.

In either case, TurboTax took care of it in 2020, and you don't need to worry about it on your 2021 tax return.

"I think what's confusing me is that $2120 is reported on the 1099-SA with distribution code 2 ==> excess contribution. That code 2 on the 1099-SA seems to say (to me at least) that the entire $2120 is an excess contribution."

You told the HSA custodian that you made two withdrawals of excess contributions: 1,600 and 500. So the 1099-SA represents the sum of the two withdrawals plus the earnings. The $2,120 wasn't actually the excess, you just told the HSA custodian that is was and they took your word for it, because they don't have any way to know better.

OK, you asked for two distributions in the same calendar year, so the HSA custodian lumped them together and put them on one 1099-SA (as they were supposed to). It doesn't matter the the 500 was excess for 2020 and the 1600 was excess for 2021.