Is sanding down the edges of the good paint, retexturing, and applying Zinsser triple thick followed by a water-based primer a good game plan to repaint a peeling bathroom wall?

I could really use some input on a project I’m tackling. I’ve got a big bathroom wall where the paint is peeling off in huge chunks. It looks like it might be the original paint from when the house was built 25 years ago. There doesn’t seem to be any moisture problems, but under the peeling paint, it’s all chalky. I’m thinking they may have painted right onto the textured drywall without using primer.

I’ve managed to peel off about 80% of the paint that came off easily. The rest seems to be sticking pretty well.

My plan is to sand down the edges of the good paint, fix up any spots that need it, then slap on a couple of coats of Zinsser triple thick. What do you think of that plan? Should I follow up with a good water-based primer before I start painting?

I’d really appreciate any feedback you’ve got.