Where, on my 2023 tax return, do i find if i have any carryforward adoption credit?

No, the carryforward for the adoption credit comes from a Worksheet.  The Worksheet looks at prior year carryforwards to determine the amount, so if you only had 2023 carryforward, you can use Line 13 from the 2023 8839.

but if line 13 and line 14 and 15 are the same amounts, then there IS no carryforward, is that right?

You are correct, if the current year credit plus the prior year carryover on line 14 is the amount allowed in the current year on line 16, then you have no carryover left for next year.