I’ve given this a bit more thought, and I believe that the 2K battery/mains doorbell only allows a trickle charge through to the battery, which in turn powers the doorbell and camera circuitry. This may be to avoid passing a significant current through the wiring, which could trigger any mechanical chime unit that is in the circuit.
If this is so then if the detection circuity draws more from the battery than the charging circuit can provide, the battery charge will gradually reduce and a more powerful transformer would not help. Cutting down the sensitivity might work otherwise a hard-wired (non-battery) doorbell might be necessary.