W-2 and 5498-SA have different info. Upon inquiry, my employer identified an issue, but said it is impossible to correct the W-2 now that it's 2022. Is this normal?

From your description, I can't tell if the employer made the contribution or not. The 5498-SA is generated by the HSA custodian, who would know how much your HSA actually received. If so, why does the employer think that they need to make a make-up contribution?

In any case, there should be workarounds in TurboTax to set you straight. Please tell us if the code W amount in box 12 on the W-2 is correct or not. In fact, if you could just tell us what the code W is as well as the actual amount contributed to the HSA through your employer (this include contributions you made by payroll deductions as well as contributions the employer made).