This script saves your current playlist to the working directory of the mpv process and works well along with autoload.lua.
Disclaimer: This is not my script. I took it from a Reddit thread and added it here since I couldnt find a script that saves the playlist and works with autoload.lua.
Thanks to @Goroto (the deleted one) and @jonniek (his muse) for the script! All credits go to both of them. Without their help, this wouldn't have existed. Thank you again!
Place this script inside your /scripts folder.
To activate the script press Alt + s.
The keybinds for this script can be changed by placing the following lines in your input.conf:
KEY script-binding save-playlist