For most scripts attached to most objects, there are opportunities to register for update, after which point you can start doing useful stuff in the script.

For scripts that are attached to weapons, I have no idea how to get started. How can I ever have anything happen?

I tried looking through any weapons that might have scripts attached to them in the game, but none did, at least, no base forms, maybe there were some that were placed in a cell and had scripts added then.

I'm kind of starting to think that script effects on weapons are no longer really a thing that's possible, given that there seems to be no way of making them happen, and there are no instances of the devs doing it either.

Scripts on weapons should still be entirely possible. For such a script, you'd need to extend http://www.creationkit.com/ObjectReference_Script

Cipscis