The standard wooden door frame is nominal 1" lumber meaning a thickness of 3/4". It is set in the opening with shim wedges and a few nails. Go to the hardware store and look at hinges for doors. The screws are no more than 3/4" long. They are intended to hold the hinges to the frame and that's about it. Metal external security frame is a bit stronger but those would be hard to come by in an interior wall, and would not be cost effective for something like a closet.
Hanging from the rough opening double stud framing is less problematic but still depends entirely on the quality of the construction which is difficult to assess once the wall is covered.
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