Yes, the limit is $6,500 for 2023, if you are under 50. Please see IRA contribution limits for details.
Your 2023 Form 8606 above shows that you made a $6,000 nondeductible traditional IRA contribution for 2023 (line 1). If you made a $6,500 contribution for 2023 in 2024 then line 1 and 4 needs to be $6,500. Line 5 will be $6,000. Your basis on line 14 should be $6,570 and will be carried over to 2024 to be used when you convert the contribution for 2023 in 2024.
Your 2023 Form 1099-R for the conversion of the contribution for 2022 shows $5,930 and therefore part of the unused basis will be carried forward to 2024 (included in the amount shown on line 14 on Form 8606).
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