I found that all search engines in Firefox, default and user-added, are stored in the search.json.mozlz4 file in the root of your profile folder. I used this software to decompress it: https://github.com/jusw85/mozlz4 (I compiled it on macOS with cargo build). I tried looking up what each JSON property means but didn't find anything, and found one comment saying that it doesn't work since Firefox always checks it for tampering.