[SwissXC90]

Did you replace the main vehicle battery or the alarm siren backup battery (internal, inside the siren)?

The backup batteries inside the siren fail after a number of years, the cure is to replace the battery or replace the siren - mounted inside the front right wheel well, need to remove wheel and wheel well cover to access the siren.

However the occurance of other issues at the same time point to possible CEM water ingress and corrosion damage, caused mainly by leaking sunroof drains.
Does your car have a sunroof?
Is the carpet wet / damp in the front? Check left and right sides. If damp / wet, then suspect a sunroof drain blockage and leak. Lots of info here on this forum on how to test, identify and correct leaking drains.

The CEM, if affected, will need repair or replacement. Repair by the guy in London is much cheaper than replacement.
To determine CEM state, remove and inspect for any signs whatsoever of water damage. Look for water marks and corrosion. It should be bone dry and maybe dusty, must show no signs of water stains whatsoever.