For All birdie badges can you take breaks or does it have to be RTA

RTA. This is a subcategory for "100%" and that has no breaks.

Speedruns are commitments, so plan for hydration, bathroom, or whatever else before you play. That should go without saying.

That said, you might find that Koopa 15 kills your run anyway, so never a bad idea to pause to attend to your needs before the next run.