I use the Chrome extension Multiselect for YouTube from the great Pollux.
I have just now moved 5000 videos from 'Watch Later' to other playlists.
Multiselect for YouTube
Chrome Web Store
Firefox Add-OnsMove, sort, and copy videos in your playlists faster and easier.
This extension will save you a lot of time managing your playlists.
✔️ Supports the new interface Manifest V3
✔️ The user experience has been redesigned from the ground up
✔️ Same display dark/light as in YouTube
✔️ Selected videos are clearly highlighted
✔️ Icon button to toggle multiple selection on/off
✔️ Action bar
✔️ Context menu
🚀 Keyboard navigation
🚀 Copy, cut and paste videos
✨ Find duplicates
🎁 Select videos with title filter