Searched for "Lightroom Catalog-v14-1.lrcat" in This PC also in my remote SSD. This is what came up.
I see a folder, but no file in that folder by that name.

Also, while looking around, it seems my internal harddrive is suddenly full (47GB/ 1TB left). In searching for the main culprits, it turns out to be Lightroom Catalogs. Could it be that my laptop just choked?
Can I delete some of these?

Searched for "Lightroom Catalog-v14-1.lrcat" in This PC also in my remote SSD. This is what came up.
I see a folder, but no file in that folder by that name.
By @NSCORP - Mark
The .lrcat.data folder does not contain the catalog file, it sits next to the .lrcat.data folder, see the screenshot below.
Your v14-1 catalog file seems to be gone, so you have to restore it from a backup. If you have not been making backups (it's mandatory), you'll have to open your newest catalog, which is v13-3.lrcat.
Backups are stored as Zip files in folders with date names.
Create a new folder, give it a name, (like Lightroom Catalog), and unzip the zip file to this folder. Then double-click the catalog file to launch LrC.


Also, while looking around, it seems my internal harddrive is suddenly full (47GB/ 1TB left). In searching for the main culprits, it turns out to be Lightroom Catalogs. Could it be that my laptop just choked?
Can I delete some of these?
You are critically low on space, and should deal with this before doing anything else.
A system drive should have at least 20% free space, preferably more, which means that you should have at least 200 GB free.
The Lightroom Catalogs are only a few GB, and are not the main culprits.
If all your photos are on the C drive, you should move them to an external drive.
LrC will then report them as missing, and you will need to relink them.
See https://www.lightroomqueen.com/lightroom-photos-missing-fix/
and https://www.lightroomqueen.com/how-move-lightroom-to-new-computer/
The relinking will be easier if you have exactly the same folder structure on the external drive as on the internal.