How to avoid / deal with rough edges after painting plywood?
When using a water based paint, you will for certain cause the grain to raise and funny things that look like tear-out on the edges.

To avoid this, before painting, I sand, then intentionally raise the grain with water, i.e. I paint it with water.

Then I sand again to remove the raised grain and the tear-out.

Finally I paint it with pigmented paint - in my case watered-down acrylic which does a nice job of letting the grain show through.