@Polaris23
The proper way to file Form 8606 is attached to Form 1040-X.
Form 8606 can be mailed by itself only when you are otherwise not required to file a tax return. See Instructions for Form 8606 which state exactly that.
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Do you have the correct taxable amount on Line 4b, and did not take a deduction?
After you e-File (you already filed)
get 2021 Form 1040-X from IRS website and mail it in with your 2021 Form 8606, which you can also get in fillable PDF.
Note: since you are not changing any dollar amounts on your amended tax return, you can leave all the lines 1-23 EMPTY.
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Part III explanation: "didn't include Form 8606 with filed return".
In your case, "my filed Form 8606 was incorrect".
You will have to mail it so this does not use up your one 1040-X e-File. (- not relevant for 2021.)
Done this way, you sign 1040-X, not 8606
