Retirement tax questions

You characterize the amount of the original contribution, not the earnings or losses.   If the contribution was $3,000 then that is the amount of the recharacterization.    The earnings are accounted for o  a 1099-R form and your explanations statement for the recharactorization.     The is no change in the tax or IRA basis.

No need to amend a do-nothing amended return.  If the IRS questions it (doubtful) just answer their letter with the facts - easier than amending.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**