If the gaps are big it’s best to get something more solid in there for backing before taping. I can’t tell how big they are, but if the gaps are like 1/2 inch or more I’d just cut some strips from some of your drywall waste and fill those gaps as best you can. Then, tape.

A little mud goes a long ways. It’s easier to add more thin coats, than it is having to sand down thick coats. When I did my bathroom I ended up doing 3 coats, starting with 6 inch blade, then 8 then 12. Then I sanded most off cause it was too thick, and did the same process but with much thinner coats. Light sanding between coats. Turned out good.

I hated it so much though that I have hired a pro for every mud job big or small since then 😂