In Big Sur, the DVD Player app lives at /System/Library/CoreServices/Applications/DVD Player.app. I don't know why.
I assume it's in the same location on Monterey.
Go there and do one of several things:
1) Make an alias of the app and drop that alias into your Applications folder. It will appear as any other app in Launchpad.
2) Drag the DVD Player app onto your dock to create a launch point there. Please see > Use the Dock on Mac - Apple Support
EDIT - adding that DVD Player should launch automatically when you insert a dvd into the drive, in any case. If it does not, then you can launch it manually with access as I described above.