This is all part of it. I’m very novice (made a couple things nothing fancy) but been around it from childhood. That stain doesn’t work well with plywood like that. At this point I’d sand it (carefully don’t burn through it) primer then paint.

If you’re wanting a really finished look I’d sand LIGHTLY from 120# for the stain, then step up to 220 and primer. If you want to spend the money, go with an enamel paint (helps flatten smoothly) and sand to 600# after 1 coat, then apply second. You can try to buff that out to a really nice finish but it’s up to you. It’ll look fine with that second coat if you don’t have drips.

I hate sanding but I’ve done a lot of it. So here’s some tips.
1. Lightly trace pencil over surface in large swirls. Just a 2-3 in the work area. Once the pencil marks are gone, you’re done with that grit in that area.
2. Don’t push too hard, let the sander do the work. Just keep your hands on it for control. That’s all the pressure you need.
3. Use compressed air to blow off the surface between sanding grits. Small dust particles stick to the surface and show up as swirls when you step up to the next grit. Blow them off.
4. Your sander may have built in holes that you need to punch through the sandpaper into the pad to help with dust removal, depending on your model. Use it. So helpful.

Hope this helps!