How to tell if a service bulletin repair was done

Hello, first post here.

We’ve owned our '03 X-type since new, multiple states (US) and dealers. We’ve recently run into problems with the AC not cooling right, new compressors and other parts didn’t fix it. Pretty sure the problem lies with the ECM.
Jag had a service bulletin, XT303-S937, which reprogrammed the ECM to reset the engine temp sensor input. Superseded XT307-S926 and XT412-S931.
I took the car to the dealer and specifically asked they do the 937 work. The dealer says they did this work last week, but they also said we needed a new compressor, which I found odd as the existing compressor was less than 3 months old. Not that that doesn’t happen, but still… The service manager couldn’t show me any paperwork that the reprogramming was done.

I’ve since been told that Jag has a DDW which tracks warranty work and recall work.

How can I get a copy for my car? The local dealers aren’t helping.

Can’t help you with your problem other than my experience with Mercedes’ AC systems when I was down looking for parts
The Mercedes’ auto wrecker told me he quit driving his Mercedes’ cars because he couldn’t keep the climate control working I couldn’t either
There to complicated and expensive when older