Applying Boolean Breaks Topology I'm trying to apply what I think is a fairly simple bool operation but I can't figure out what the problem is or what to do to remedy the situation.

When modling with the modifiers in place it looks perfect. Exactly what I want to see:



However, when i apply this to the object, the topology is entirely ruined:



The underlying topology looks like this:



I have absolutely no practical experience using booleon operations so far in my Blender journey and I have absolutely no idea what to even attempt to fix this situation.

What should I start looking into first?
Judging from the rounded surfaces and the post-application deformations, I'd wager that you have an unapplied Subdivision Surface modifier. Once you've applied the boolean operation without applying the subsurf, the subsurf operation is now operating on the circular cutouts as well as the original mesh.

Consider not applying the boolean operation if possible. One of the biggest advantages of the boolean workflow is the procedural aspect of it. If not, backup the model and apply all other modifiers before applying the boolean.