Then I read a little closer, and realized I pretty much just had to add an "i" onto all the underlying mysql functions ("mysql_" to "mysqli_"), at least for the ones I was using commonly.
I'm still in the process of migrating that project, now on 7.4, to a modern Symfony framework, but I tested it out in 8.1 the other day, and it needed...1 change to work apparently perfectly.
I'm still going to need to do more thorough testing before I put production on 8.x, but with 7.x now unsupported, that has become a priority.