No, the Roth conversion amounts don't count as Roth IRA Contributions, so your Prior Year Roth Contributions would only be any amounts directly contributed to your Roth IRA.
From investopedia.com:
"The funds that you put into the Roth are considered converted funds, not contributions. That means you have to wait five years to have penalty-free access to your funds in your Backdoor Roth IRA if you’re under the age of 59½.
Such converted funds differ from regular Roth IRA contributions, which can be withdrawn at any time without taxes or penalties."
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"
