That seems to be a common misconception. Again, the IRS views all your Roth IRA accounts as if it were one account. It doesn't care about account boundaries. Same is true for IRA accounts .. they are all one. (however, not true for 401(k) accounts).
The OTHER 5-year rule on conversions and penalty for withdrawing principal does start a new clock for each conversion. However, the 5-year-rule on conversions does not apply to those over 59 1/2.
https://www.schwab.com/learn/story/what-to-know-about-five-year-rule-roths
