I realize I am not exactly answering the OP's question about where to put captured long term cap gains, but it made me wonder about something else.
(btw, OP, the tax brackets for 2022 are up on the aarp.org site along with a comparison to 2021.)
For what it's worth -- I don't see a big need to be paranoid about higher cap gain taxes -- any time soon. When the gold-hawkers show up in ads, it always looks to me like they are opportunists trying to create and then tap into fear and a sense of urgency -- for their own gain.
If your gains are inside IRAs, I am sure you know that taking a bigger than needed RMD could bring on IRMAA. If you are charitably inclined, you could look into using QCDs to lower your AGI, and maybe head off IRMAA at the pass. (I am pretty sure that if you go even a buck into IRMAA territory, you are had.)
If those cap gains are residing in regular accounts, not tax-deferred, and you decide to capture them, there will be no QCD opportunity to rescue you from IRMAA. And IRMAA waits two years to get you -- just when you might have forgotten all about it.
But if you are all set to take a tax hit anyway -- there could be another angle on where to take gains -- but only if they are inside IRAs right now.
If you like what you own inside IRAs -- especially if you have owned the investments forever and the gains are big enough to stand a bit of a hit and still look good, and, most especially, if there are stocks that have been paying and increasing dividends for decades -- well then.....breaking up could be hard to do......
So......would a conversion to Roth (after RMDs or QCDs) possibly be the way to go? If the conversion could be done in-kind, you could still keep your favorites -- even though you would have had to pay taxes on their current value. But then they could be tucked away inside a Roth, never to be taxed again.
Warning to any readers out there: I am not a CPA or a financial advisor of any kind, so please do not take tax advice from me because I don't actually know what I am talking about. But I might give you some ideas about things to think about or check on.
Boomer
PS: If I am wrong about IRA conversion to Roth being a possibility, albeit a taxable one, after RMDs are covered, somebody please tell me. Maybe things have changed on that and I missed it. Also, am I right about in-kind conversions to Roth? (Hey, retiredguy123 -- I'm talkin' to you.

Am I right about what I am saying about conversion to Roth still being a possibility after RMDs are covered?)