Question about Ugreen CM403

In short: Yes, most of the time.

Long: Most on-board entertainment systems use a combination of a 3.5mm plug with stereo signal (insert adapter here) and a 2.5mm plug with voltage on it. With these systems, this can be plugged directly into the 3.5mm socket.
Bluetooth is currently permitted on most flights and is therefore not a problem.

Further input: the entertainment system can often be accessed via Wi-Fi and you can watch films from your own smartphone, tablet or laptop. Some travel companies only rely on this.

If in doubt, check the information page of the relevant airline.

Bluetooth should not really be a problem in the aircraft and also works in the mobile phone's flight mode.

I think so, Bluetooth is normally allowed

I don't know that