It's important to let Vortex move the "Mod Staging Folder", since if you do this manually it's a good chance all installed mods will be duplicated and you'll lose all the conflict-rules.
So basically, you should do something like this, where let's say you first select SSE:
1: On Vortex mods-tab, click "Purge" and afterwards exit Vortex.
2: In Steam, move game to another disk.
3: Run game launcher to setup registry etc.
4: Start Vortex, you'll get a message about game moved.
5: Just to be on the safe side, re-start Vortex.
6: Make sure new location of game is detected in Vortex.
7: Under Vortex - Settings - Mods, type-in a new location of "Mod Staging Folder" to be on the new disk.
8: Let Vortex move all mods for you, this can take some time.
9: Under Vortex - Settings - Mods, make sure you're using "Hardlink Deployment".
10: Under Vortex mods-tab, click "Deploy".
11: If you want to move another game, in Vortex switch to another game and start on step 1 again.
For step 1, the main reason to use Purge is to speed-up step 2, since if you don't purge the mods you'll copy all active mod-files twice, first in step 2 and afterwards in step 8. A minor reason is, it's possible some of the files isn't correctly handled afterwards, meaning even if you disable or uninstall mod the files will be left behind.
It's possible you can move multiple games at once, but it's safer to take only one game at a time.
Note, if you Purge and switch to another game, Vortex will re-deploy game before switching to another game, making the Purge a waste of time.