The pro-rata rule does not care which dollars you converted. It looks at every traditional IRA you own on December 31 and taxes you on the mix.
Roth IRAs have an income limit. The ability to contribute directly phases out across a band of modified adjusted gross income — a lower band for single filers, a higher one for married couples filing jointly — and the IRS adjusts both most years for inflation, so look up the current ranges rather than trusting a number you read once. What has no income limit is making a nondeductible traditional IRA contribution, and what also has no income limit is converting a traditional IRA to a Roth. The backdoor Roth is simply walking through that gap.
— Educational, not financial advice.