In "\Steam\steamapps\common\Portal 2\portal2\puzzles[17-digit]\", I see a bunch of .p2c_12 and .p2c_13 files. Are these auto-save or back-up files of some kind? Can I safely delete them without it affecting something else?

Edit NM

No, the PTI maps are normally in P2C files.

Wildgoosespeeder, try moving those files to your desktop and launching Portal 2. See what's different. If it's bad just move them back.

These seem to be older versions of the same maps. In addition, the data format in the p2c_12 files differs substantially from the others. (Open them in Notepad and have a look.)

My theory is that the P2C file format got changed at some point and these files are backups made during the conversion process. If I look at the timestamps of the files, the p2c_12 and p2c_13 versions of a map always have the exact same timestamp, which is (much) older than the "normal" P2C file. So they were probably made at one point in time and are not continually updated.

I think it's safe to clean them up, but first move them to a different folder and see if your maps still open and compile properly.