Roth IRA conversion via 60-day rollover

I took $22,000 out of my traditional IRA in late December 2022, and put it in a non-retirement (checking) account.  In January I realized I could/should have done a Roth IRA conversion.  The IRS pubs say you can do a 60-day rollover from any retirement plan to any other retirement plan, including a Roth IRA conversion.  But Form 8606 asks "enter the net amount you converted from traditional, SEP, and SIMPLE IRAs to Roth IRAs in 2022".  Can I still put the $22,000 into a Roth in January 2023 and have it count as a conversion happening in 2022?  (I know I have to pay 2022 taxes on the $22,000).  If so, can I have a reference to the pubs backing that up?  Because some financial institutions I've been dealing with (Fidelity, Vanguard) seem to think it is impossible.