I can run the first version of the source hunter DLC (divinity_original_sin_dlc_source_hunter_2.0.0.1), but not the latest version (divinity_original_sin_dlc_source_hunter_2.5.0), because the installer insists that the base game was not detected and I had to install the GoG version of the game. Which I have, of course.

Only possible reason I can think of is that I don't have the game on C: because of space issues on the ssd. But the installer knows about the location. Not that I could change anything in the installer settings right now, since it won't let me log in with the exact same account with which I am logged in here...

You shouldn't need to re-run the DLC installer. All it does is place a couple files in the '..\Documents\Larian Studios\Divinity Original Sin\DLC' folder, so if that folder still exists the Source Hunter DLC should be active in-game (on the main menu select 'Additional content' to check). If you renamed that folder or are playing from a different Windows account, then you should just be able to copy the DLC folder from your previous My Documents D:OS folder.

There is no 'Additional content' in the main menu.
There is a folder 'DLC' in the D:OS folder with two files (called 302050 and 302051) of the type 'file' (haha), which are both 0 bytes.
I did not move or rename anything and I do not use a different account.

The first thing I tried to install was of course the newer version, which is also the only version on the download site these days. Since I still had an older version in my files, I tried that out of curiosity, when the newer file didn't find my game installation. I also re-downloaded it, in case of a corrupt file, but no luck.

It should be the third button from the bottom, above 'Options' and below 'Profiles'. Make a copy of one of the existing files and rename it 322490 to enable the companion DLC.

Could you have accidentally installed an old version, or not installed the patch(es)? Check the number at the bottom of the column of buttons in the main menu (latest is v1.0.252.0).

Try re-installing the game by right clicking the setup_divinity_original_sin_2.14.0.26.exe file (assuming you downloaded the latest full installer) and running as administrator.

Hm, is it possible that there's problem with the numbering of the files? My version is 1.0.57.0, which seems to be a higher version than 1.0.253.0, but apparently it isn't.

Also, in my archive I have a setup_divinity_original_sin_2.14.0.26.exe and a setup_divinity_original_sin_2.3.0.6.exe plus a patch patch_divinity_original_sin_2.3.0.7.exe, where the latter one again looks to be the higher version number, but when I look at the date of the files, the former one seems to be the latest version.

Oh, I see now that the latest file on the download page is called 1.0.252, but when I try to re-download it, it is the 2.14.0.26. Can you blame me for being confused? ;)

Gonna re-install now, thank you for your help, Raze!

Edit: Yep, that was it, problem solved. :)

You may have figured this out, but with the version numbers they are compared as numbers, rather than decimals, so you can't add trailing zeroes (57 < 252); you can add leading zeroes, though, for comparison (1.0.057 < 1.0.252).

GOG names the files based on the version of the installer, rather than the game.