The OP purchased the towbar and TRM from me. I fully tested the TRM in my car (which already had a TRM fitted) and it worked perfectly so the TRM itself is not specifically programmed to the car. I've just tried disconnecting the green connector from my TRM which resulted in 2 errors appearing about trailer module and rear park assist. This tallies with Clan's explanation that the dealer removing the electrics must have disabled the functionality to prevent the message appearing.
Whether getting a dealer to re-apply the software to the car is sufficient to work with existing TRM I don't know, but its probably worth a try in the first instance as it sounds like it needs happen anyway. If unsuccessful, the probably new TRM (minus the loom may be the solution). Nothing seems straightforward when it comes to Volvo electrics these days
. On the P2 models, the TRM was plug and play and only required a software update to disable the car foglight (if the driver so desired that option).