I'm having the exact same issue. Here's what I'm seeing on my end, which is NOT an answer.
The form where it's supposed to be showing your carryover amount and other details is Form 3800 Part IV. I figured this out by reading through all pages of Form 3800 in Forms View and on a desktop version of TurboTax. Instead of performing your override on Form 3800, Part I, line 4, you could populate Part IV (via overrides) which will then ripple through to Form 3800, Part I, line 4. But again, this solution also involves making overrides!
The part that TurboTax was able to handle correctly for me was in the "Carryover Wks", line 18 ("General Business Credit"). The column labelled 2022 does indeed show the correct amount that needs to be carried forward into 2023. Where I think TurboTax fails is what I've described in the previous paragraph.
I'll venture to guess that this is a bug.
Standing by for an expert to chime in.
