The filing deadline being extended to 11/16/2023 has nothing to do with your situation. If you do a Roth conversion in 2023, it reportable on your 2023 tax return. Roth conversions are performed in a particular year, not for some other year.
$6,000 plus gains was the amount transferred to accomplish the recharacterization, not the amount recharacterized. You recharacterized $6,000.
