Is it safe to delete logcat.txt files or the whole psysinfo folder to make more space on my Android phone?
It shouldn't be a problem to delete them if there are only .txt or .log files. If you are not sure, delete a few files with smaller to medium sizes. Restart your phone, and check if all apps are working normally. If they are, then proceed with deleting the others.

Log files are used mainly for debugging purposes. Deleting them should not bring chaos onto your phone.