Hello MacMonkeySmith,
Thanks for asking the Apple Support Communities for help with an external DVD player.
Please start with the guide here: DVD Player User Guide Troubleshooting - Apple Support
If using the Apple SuperDrive, you will need an adaptor: Apple USB SuperDrive - Apple
"*MacBook, MacBook Air, and MacBook Pro models with USB-C ports require a USB-C to USB adapter (sold separately) to use Apple USB SuperDrive."
Use one of these adaptors based on your computer connections: How to connect the Apple USB SuperDrive - Apple Support
"To connect your SuperDrive to a Thunderbolt 3 (USB-C) or USB-C port on your Mac, you can use one of these adapters:
If your ports are not working for other items, it may be beneficial to reset the SMC on your MacBook Air: How to reset the SMC of your Mac – Apple Support
Also check your settings. Please be aware, a DVD will not show up on the Finder unless you enable the setting in Finder > Preferences > General > Show these items on Desktop.
If using a third-party DVD player, please verify the DVD player supports macOS Big Sur. Contact a third-party vendor - Apple Support
Thanks and have a wonderful day.