showler

Vortex generally doesn't move mods the game folder.  It makes links to the files in the staging folder.
Copying the game folder with those links still in place is bad and creates problems.
Correct method is to "purge" mods from game folder and then "deploy" them again as needed.

Those all indicate that Vortex is having difficulty communicating with GitHub.

I don't see the main FOOK2 files in the directory.
Make sure that you installed "FOOK v1-2 Open Beta Data Files".
Also, you seem to have a "data" folder inside your "data" folder.  Check that to see if any of your mods got installed wrong.  Sometimes a mod with a bad folder structure will create a new "data" folder instead of going in the existing one.

Start by clicking on all those "failed" extensions to find out why they failed.

Many game extensions are included as part of Vortex.  Most are hidden behind the "show bundled" button.  Some are visible because they are getting more frequent updates than usual.  If the extension keeps reinstalling itself that means it is considered "part of Vortex" rather than an optional extension.

Either it's a LOOT rule or the rule is based on the category the mod is placed in.

Set your download directory to match your existing one and you shouldn't need to redownload anything.
You'll need to reinstall them because you don't have the information Vortex needs for that anymore.

Our friend Pickysaurus has you covered.
https://www.nexusmods.com/site/mods/120

You can't delete anything in the deployment folder.  Those are the real files, the ones in the game folder are just links to those files.
You can delete the downloaded archives, but if you need to reinstall or change the mod you'd have to re download it.
FYI, the files in the game folder report a false size when you look at them.  They show the size of the real file but are actually extremely tiny.  It gives the false impression that you're using more disk space than you are.

You don't.  They're part of Vortex.

I believe it uses the newer of the two files, the one in the game directory or the one in the deployment folder.
So if you have a case where the file has been replaced by an older version somehow it will keep the newer version rather than either saving all or reverting all.

Why do people keep thinking this is a problem?
Vortex comes packaged with extensions for dozens of games.  If it keeps re-downloading and re-installing the extension, that's because it is supposed to be there.  It's part of Vortex.
The extensions are tiny.  Just leave them alone.

For now you can unpublish them, I believe.  Pretty much the same as making them hidden.

The reason why you purge your mods is that the files in your data directory are not real files, they are just links.  But if you copy them to another drive, Windows will treat them as real files and you'll take up more space than you need.  Also, when you restore them later Vortex will be confused by them now being real files rather than links.

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.