Is the new m2 macbook air 15 inch compatible with a 2015 apple usb2 dvd drive

My wife is considering updating her 2015 era MacBook Pro to the new 15 inch M2 MacBook Air. She occasionally plays CD's on an external USB 2 DVD drive that we got with the MacBook Pro. The new Air uses Thunderbolt 4/USB 4 ports, which the local Apple store tells me is mechanically incompatible with USB 2. If we get a USB 2 female to USB 4 male adapter, will that DVD drive work with the new Air? I don't know if the driver for the DVD is a kext file included with the OS, or is in a ROM somewhere.