PS4 controller (V1) enormous input lag (Android 10) with Bluetooth?

I really want to use my controller on my Redmi Note 8 (Miui 12). Unfortunately, the mapping is wrong in some games, i.e. If I press x, for example, I'm sent to the home menu. In addition, the games are unplayable because of the input lag, which is otherwise annoying. However, I hardly have any problems with cables. My questions are: What could be the reason (e.g. Old controller, only for V2 controller, operating system, Bluetooth not sufficient) and how you can fix it e.g. Mapper, knock controller on the table, save on an Xbox Elite or new mobile phone.

I had a similar problem. It did it by just charging the controller, no idea why but it helps.