No. You don't need to work the form 8962 manually. You can amend your 2022 tax return to add the 1095A information using the HSA topic in the the "Deductions & Credits" section. Adding the form 1095A information will generate the form 8962.
So after completing the amendment you will be given the option to "Print/Download" your return. After the download you can view the pages and find the form 8962 for printing. Then you can send in the form 8962 and a copy of your 1095A as requested by the IRS.
Here is a link on amending a prior year return in TurboTax.