Yes, your entry for 2023 looks correct. You do not have a entry on line 2 because you do not have a basis on line 14 of your 2022 Form 8606.
No, Form 8606 will not add the total of all your backdoor.
Please see How do I enter a backdoor Roth IRA conversion? for additional information.
Your 2021 and 2022 Form 8606 seem correct, except you should have $6,000 on line 14 of the 2021 Form 8606?
Did you make a $6,000 nondeductible contribution for 2020? And you made a $6,000 nondeductible contribution for 2021? And converted $6,000 in 2021? If yes, then you would have $6,000 on line 1 for the 2021 contribution and $6,000 on line 2 for the prior year basis on your 2021 Form 8606. Line 14 should be $6,000 and this will be carried over to the 2022 Form 8606 line 2.
You made a $6,000 nondeductible contribution for 2022 and converted $12,000. Therefore, you do not have a basis to carry over to 2023.
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