No, the IRS will not automatically figure the Child Tax Credit for you on your 2021 tax return. You must determine the amount of the Child Tax Credit for which you are eligible and claim it yourself. To do this, you need to use Schedule 8812, Credits for Qualifying Children and Other Dependents, and follow the instructions provided by the IRS. If you make a mistake in determining the amount, the IRS will correct it and notify you of any changes.
Sources:
Publication 596 (2023)
Publication 5534-B (06/2021)
Publication 971 (12/2021)
Publication 17 (2023)