Tracking your YouTube "Favorites" playlist with RecoverMy.Video APP is not that convenient as with RecoverMy.Video. The reason is that RecoverMy.Video APP is not able to access authenticated content like your "Favorites" playlist. But there's a workaround (And another workaround for private playlists).
Depending on your YouTube interface language setting it is possible or not to change the privacy setting of your "Favorites" playlist. If it's possible the easiest way is to put the privacy setting from "private" to "unlisted".
Check this how-to article how to set a "private" playlist to "unlisted".
Changing the YouTube interface language on desktop to "English (US)" worked to display the privacy setting dropdown. So it makes sense to switch to "English (US)" in order to use the privacy setting and then switch back to your former language setting. Your "Favorites" playlist will keep the adjusted privacy setting.
Some user may experience an error message "Unlisted privacy is not supported for the playlist. Please use public or private." when trying to set the "unlisted" setting for the "Favorites" playlist on YouTube. If you see this message then you have to go with "Option 2" or set the "public" privacy setting.
If option 1 is not an option you have to copy the videos of your "Favorites" playlist to a new "public" or "unlisted" playlist.
The obvious disatvantage of this copy process is that you have to repeat it from time to time to cover newly added videos to you "Favorites" playlist.