e-filed amended 2022 federal return with stock plan transactions supplement form

This was my first year filing with RSU that I sold form e-trade. However the first time I e-filed (both federal and state (california )) I forgot to include the Supplement form that included the adjusted cost basis. The first time I filed I owed $3k, which was debited from my account, however shortly after noticing that I missed this crucial form after a day or so, I went in to amend my federal and include this form, I'm now showing that I didn't owe nearly as much as I had thought and substantially overpaid. When I amended I e-filed both as well. I don't remember all of the steps but at the end it gave me forms to print and mail.

Do I still need to mail anything in if I had e-filed for both initially, as well as my amended federal? Or should I just expect a delayed check or credit back to my checking account that's on file? (this is for filing last year 2022)

thanks in advance