Key has an RFID or similar chip. Older models the chip was a little box you could move between keys. The diamond model the ID is a soldered on chip.

The battery is almost never the problem. I refurbished a few of these and reflow the solder is what fixed them. For a while. Eventually i bought a new key and was the best $ ever spent on my e 53

True, but bmw key recharge batteries from back then do have a life span and we are talking over 20 years. Not difficult to replace the battery either. If you can get a new one then you do feel good about it and never have to worry about it for the rest of the lefe with the car. Especially if you are in your 60’s/70”s.

Yes it's worth changing the battery but reflow the bad solder joints. All my keys needed it.