OK, this is VERY important.

When the compressor goes out, it generally contaminates the entire AC system- evap valve, lines, condenser and evap are all fouled wit shrapnel. These bits can circulate if not meticulously cleaned out, and cause failures a year, two or three later. The dealer will of course say these subsequent are unrelated to anything they did.

On other cars Ive worked on, there are detailed work instructions (TSBs) on cleaning/flushing the system. Not sure about BMW as Ive (thankfully) not had to get into any of mine.

You can assume the dealer will do the job right...but personally I'd have tried to express my concerns such that the mechanic takes his time and does it right. Not sure how....write up a note on it, have a chat with the actual mechanic, etc.... not pushy or accusatory, 'just have concerns and want to hear what you'll be doing to make sure...'