Steam Workshop can be finicky with AwSW sometimes. It's possible that the mods never downloaded, or that the mods are in your Workshop Download folder but never got installed in the Mods folder of the game.

One thing you could try is uninstalling everything except modloader, then see how it runs alone.

If you're willing to get hands-on, then the place Steam puts AwSW's workshop files by default is C:\Program Files(x86)\Steam\steamapps\workshop\content\571880. If you can navigate to your computer's equivalent, you can just copy it all to SteamLibrary\steamapps\common\Angels with Scaly Wings\game\mods.

You probably want to back up your game before doing anything like that, though. I've never had trouble with this method, but I can't guarantee it works for everybody. I am a mod user, not a mod maker.

Edit: Also, don't forget to try right-clicking the game in your Steam Library, click "properties", and look for a button that says "verify integrity of game files". It may help if you're having any issues.

There's probably also a lot of old information on the threads here, if you want to find info from someone who knows more about the inner workings of modloader. Believe me, this is not an uncommon problem.

Slight progress has been made.
Now, the MODS button shows up.
When I click it, it says I have Core, MagmaLink, and Side Images. Which are a fraction of the mods I actually subscribed to.
When I click Add Mod from Workshop, the game freezes. (Not Responding)
So I still need some help.

The easiest way to get a clean state with awsw is by unsubscribing from all mods, starting the game, closing it, and then resubscribing to the mods you want via the steam client

Ok, that helped a little bit, Blue.
I'm installing mods back in, one by one, to see if any one particular one breaks anything, and..
I'm noticing a pattern.
No matter what mod, whenever I close the MODS menu, the game freezes (Not Responding) within the next couple seconds.