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Most common cause of this is SKSE (or another mod that gets installed to the base game directory instead of the data directory).  You can try reinstalling it, at which point Vortex should tell you whether or not there's a conflict that needs to be resolved.
Otherwise manually installing SKSE instead of letting Vortex do it usually fixes the issue, but shouldn't really be necessary.

The staging folder or the downloads folder?
Because the staging folder is not "copies of the archives", it's the actual installed mods.  It's the only place they exist.  The "files" installed in the game directory are just virtual links to the actual files in the staging folder.
Now, if you meant the downloads folder then that's different.  Deleting them shouldn't affect your mods.

In that case Vortex should be warning you that the files in the data directory have been modified outside of Vortex's control.  That warning should come before the purge is done and give you the chance to either keep the changed files or revert to what's in the staging folder (the files that came with your mods).
That's why I set up bodyslide to output the files to the staging folder as a new mod so that I can make it override everything else.

An ESM will be in the top group by default.  If you need to move it anywhere further up you can use the conflict resolution rules to move it where you need it.

It's normal.  They use extensions to update Vortex functions without having to update the entire program.

This usually involves a mod that is installed to the root folder (script extender, enb, etc.) that has a conflict with a mod that is installed normally.  Picky mentioned at one point that if you reinstall those types of mods newer versions of Vortex should flag the conflict and allow you to resolve it properly.
 

You're not looking for "move staging folder", you're looking for "mods staging folder".  Changing that will cause Vortex to move the staging folder and all mods in it.
And make sure you're choosing "mods" from the top list of tabs after hitting settings (should be "interface/Vortex/mods/download/workarounds/theme"), not from the list on the left.

80 or so mods on your available games list usually means that your computer is having trouble connecting to GitHub.  You are only getting the built-in game support not the list of available extensions.
You could try white-listing Vortex in your firewall or using a free VPN to test this.

Try changing it in the deployment folder if you can and then redeploy.  That should skip the "changes outside Vortex" issue.

Might be worth turning off the GPU acceleration in the settings as a test.

Your version of Vortex is too old to auto-update.
You'll need to download the new version and install over the top of your existing version.  It shouldn't result in any lost data.

There was an issue similar to this a while back that involved the installation of SKSE.  I think manually installing SKSE instead of letting Vortex do it was one solution.
It wasn't just SKSE, it could happen with other mods that are installed in the main folder rather than the DATA folder as well.

The extension is included for everyone.
Your error is different.  Your computer is unable to connect to GitHub to download and install the update.

I don't think that's the problem.  The author of the first mod suggests an overwrite and since their files are loose and the other ones are in the BSA it should be automatic.
You may be having a texture problem or something else might be interfering.

Vortex info is stored in your %AppData% folder in your user folder.

You should be able to right-click the mods you don't want in the Collection and tell Vortex to "ignore" them.

A game having a mod section on the website DOES NOT mean it is supported by Vortex.

That's the code for having gone over the server request limit.  You'll be restricted to a small number per hour until the next day.

MO2 wurde nicht ersetzt. Vortex wurde von Nexus Mods unabhängig von MO2 entwickelt. Es war jedoch der Entwickler von MO2, der Vortex erstellte, und er betrachtete es als Verbesserung von MO2.

Using the default deployment method the mod staging folder has to be on the same drive as the game.   The downloaded archives can be on a different drive.
However, since it uses links to deploy the mods rather than moving the files, it doesn't actually take up double space.  One file is real, the other is just a pointer to the real file.

There's three folders.  Game folder, mod folder (deployment folder) and download folder.
You've said "game folder" and "mod folder" but not "download folder".  The download folder defaults to your AppData folder on your C drive. Did you move that to the 4TB drive as well?

Yes, not connecting to GitHub will prevent you from updating certain features of Vortex.
But that's a result, not the cause.  If Vortex is connecting to Nexus Mods but not GitHub it's not a Vortex problem it's a problem with your internet connection.
Can you access GitHub with your browser?
Try a VPN.  If that fixes the issue then try contacting your ISP and find out why you are having trouble connecting to GitHub.

You need to install the version I linked and then install the newer version on top of it.
From what I could find the error you were getting was because the newer version was missing files from the earlier version that it needed in order to remove and update the earlier version.  Therefore you need to "fix" the earlier version by reinstalling it and then install the newer version on top of the now "fixed" older version.
 
edit: Also Pickysaurus is a staff member at Black Tree Gaming, the developers of Vortex.  He provides most of the installation support on the forum, though he can bring it to the attention of the Vortex developers if he feels he needs to.

You should have the Starfield extension for Vortex installed.  It's the extension that tells Vortex how to install the mod so that individual mod authors don't have to worry about it.