90% of the time it’s a bulb. Are you sure ALL the bulbs are flashing on the left side and that one bulb is not out? I mean physically check rather than relying on the indicator on the dash. The other thing that can cause this sometimes is LED bulbs but you said you changed them all. Also clean your grounds as they can cause many spurious issues. Finally swap out the relay, it’s a simple circuit so not much else to check.

“When you activate either flasher, the parking lights come on” - This is normal on most all German cars, it’s a safety feature when the car is parked curbside overnight.