This is something that I've noted as well, and in looking at the support documents for Apple, I cannot find where you can highlight text in Notes any longer. When I try to highlight, which I know you probably have already discovered, it does not highlight over text, but if I wipe further down on the page, you will see something appear. It is almost as if you can not use any of the markup tools in the text area itself. I'm still looking, but you can see if anyone else responds here.
Okay, did a little more digging, and it appears that it is impossible to highlight the typed text in a Note. You can only highlight a scanned document or something like that. The Markup does not allow you use the tools in the typed text area in a Note. You can provide feedback to Apple to let them know you would like to see a change by going to Feedback - iPhone - Apple