I have the same refrigerator (cooling unit) in a couple RVs.
Reminder: The RV needs to be mostly level to work properly. I've noticed that when I'm not level (even a couple of times just parked on the side of a residential street with some curvature to it) sometimes the freezer section gets cold but the refrigerator section doesn't get as cold as it should.
Also, testing a refrigerator really takes many many hours. Things associated with this type of refrigerator don't change (cooling) instantly.
I suggest doing a couple of tests...
While level, put it on propane only and leave it for at least 12 hours. Put a thermometer in both the middle of the freezer and one in the refrigerator and then leave it alone except for very quick checks along the way. You'd like your freezer to be around 0 degrees F, and the refrigerator to be less than 40 degrees F.
Then, turn off the gas and leave your refrigerator open for an hour so it can drift back to room temperature. Then turn off the gas and plug in to shore power and run the same test for 12 hours.
I'd be curious to hear the results.
I had that same cooling unit go out on me about a year or so ago. Here is a great thread with lots of testing, advice, info on cooling unit replacement, and a happy ending.
https://www.rv.net/forum/index.cfm/f...g/1/page/1.cfm
(hope it's okay to post that link here...just trying to be helpful)
Good luck!
Chris