No, you do not need to amend your 2023 taxes, assuming you entered the nondeductible contribution of $6,500 on your 2023 return. You should have a 2023 Form 8606 with a $6,500 basis on line 14, which will be carried over to line 2 of the 2024 Form 8606.
You cannot deduct your loss but if you convert the funds with loss then you will have a basis left on line 14 to use in the future. In your case, assuming your value was $0 at the end of 2024, you will have a $502 basis on line 14 of your 2024 8606 to use in a future year.
Please review How do I enter a backdoor Roth IRA conversion?
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