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Yes, I did this recently.
I flew in on Etihad First Class but the connection was in 2 cabin Business.
I was able to enter the First Class lounge and restaurant.
Didn’t have any issues during my 12 hour layover except 1 time, when I had to explain the policy to the door person and asked them to speak with their manager since they weren’t familiar and didn’t want to let me in.
Make sure you retain the boarding pass with the first class segment just in case.