Do I need to inform TurboTax of my error on Form 1040SR when filing my 2020 federal return?

There is no  need to update your  return in the TT program however if you do then you MUST save a PDF of the originally filed return  before using the amendment process.  

What was the error?  Did you receive a letter or notice from the IRS? 

Any adjustment made to the filed tax return by the IRS does not need to be reported to TurboTax.  

Only a calculation error would need to reported and then only if the IRS is charging you penalties and/or interest based on the calculation error.

Did this have anything to do with the Recovery Rebate Credit on the Form 1040 Line 30?

Do you know if it will affect next year when you transfer into 2021?  Will you need to carry it over?  If not just keep the paperwork with a copy of your tax return.