showler

You're not actually losing that space.  It's a false report by Windows.
If you have a 1TB drive and you install 200GB of mods you should be able to put 1.2TB on the drive as far as Windows is concerned.

First, you can install a free VPN to see if your ISP is interfering.
Otherwise, follow the directions here:  https://help.nexusmods.com/article/92-im-having-download-issues-what-can-i-do

To be clear, the mods need to be installed on the same drive as the game.  Not Vortex.
You can set a directory for the mods for each game in the settings.

Vortex INSTALLS the mod.
Modengine2 makes the game capable of using the mod.
Similar to Bethesda games where Vortex can install all the mods, but some of them are going to need the script extender in order to function.
It's not misleading...it's two different functions.

Masterlist errors usually result from failure to connect to GitHub.
Try a free VPN and see if it fixes the problem.  That will tell you if your ISP is messing with things in a bad way.

There are mods for thousands of different games on the website.
But Vortex can only install mods for a few hundred of them.
Others might need a different mod manager, or it might need you to place the files in the right place on your own.
Pick a mod for the game and read the mod page to see if they give you installation instructions.

".f4se" files are called co-saves.  There should be one for every regular save.
".fos" files are the actual game saves.
The game save file saves all the information the game normally uses and the co-save saves the information used by F4SE based mods that need to store extra information.
If you had a similar incident to me, you'll need to go into your Steam install folder (something like c:/programfiles(x86)/Steam), then find a folder called "userdata" and then you'll find a bunch of folders with numbers for names.  Sort by most recent and check them until you find your .fos save files and then copy them back to your "my games/Fallout 4/saves" directory so that they are back with the matching co-saves.

Neither of those games are on the Supported Games list.  The website hosts mods for a vastly larger number of games than Vortex can manage.
https://www.nexusmods.com/about/vortex/#:~:text=With mod support for over 30 different games,Vortex is the most versatile mod manager available.

Ask here: https://www.nexusmods.com/site/mods/196

On the Extensions tab, click the "show bundled" button and check if any extensions are disabled.

Your steam install directory is probably something like "c:/program files(x86)/steam".  Inside that folder should be one called "userdata" and inside of that should be a bunch of folders with just numbers for names.  You'll be looking for a recently modified one that contains your save files (which will end with .fos).
You'll need to copy them back to your "documents/my games/fallout4/saves" directory.

Have you tried setting the Skse launcher itself as a game in Steam?  And then setting the controller options for it specifically?  Steam has PS controller support for all games, only games with native support or only games WITHOUT native support.  You might need to play around with the various options to find one that works.
Or, and this is a sudden thought, it could be connected to the issue Pickysaurus mentions here: 
Specifically where he says "in Skyrim 1.6.1130 the integration with Steam appears to be completely absent".   If so, this might be a bug that Bethesda will need to fix.
 

Check in your steam install directory under "userdata" and sort by most recent changes, then check the numbered folders for files ending in ".fos".
I had the same thing happen last night and Steam had moved all my save files from the Documents folder to that folder in the Steam install directory.  Moving them back fixed everything.

I'm not sure it has that option since what you are experiencing shouldn't be possible.
Best bet might be to use the "purge" option on each game to remove the links, then manually remove the mods from the folder, copy back only the files for a single game, have Vortex move the staging folder and then repeat for the other games.

Did you update SKSE?
There was an update for SKSE and an update for Skyrim SE today.  You should check what version you have of each.

Windows treats hardlinks as real files during a copy procedure.  Purging your mods would have temporarily removed the hardlinks and avoided the problem.
Under normal operation the hardlinks take up a tiny amount of space.

BG3 is a Nexus Mods created/maintained extension.  It is currently being updated frequently so it is listed as a "non-bundled" extension.  However, it will eventually be added to the bundled extensions that are automatically updated because they are part of Vortex.
There are dozens of these extensions in Vortex.
Don't worry about them.  They are needed and they do no harm.  You will not be able to remove them.

It's not listed as a supported game.

Because they are part of Vortex itself. They are treated as extensions because it allows them to update separate from the main program, but they are part of the full Vortex package.
 
Stop trying to uninstall them. It won't work.

One click Collections are reserved for Premium subscribers due to the need to serve ads to ad-supported subscribers.

It got separated to different tabs because the "mod staging folder" is game specific while the "downloads folder" is universal to all your games.
 
It was, arguably, more confusing having them on the same tab while behaving so differently.

The extension was hidden because it did not work properly and I thought Picky had turned off the mod manager download button.

If you don't do the tests here ( https://help.nexusmods.com/article/92-im-having-download-issues-what-can-i-do ) then they'll just ask you to run them and your help will be delayed. Run them now and post the results to save time.
 
Also, if you can, try a VPN and see if that helps or not.