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MC passing out after killing the Big Bad or otherwise completing their major goal is Post-Victory Collapse, which explicitly calls out what you said about "commonly used so the author doesn't have to write about all the boring clean-up after the battle climax."
Your example for The Hobbit has an entry under Offscreen Moment of Awesome, since Bilbo collapsed sans any victory or awesomeness, but since he's the POV character it resulted in the actual awesome being offscreen.
there's Waking Up Elsewhere
Working on cleaning up List Of Shows That Need Summary
Post-Victory Collapse is mainly what I was after, but Waking Up Elsewhere covers what it misses. I was reading a book series where the MC seems to pass out after the climatic battle at the end of each volume, but one time he lost the fight and the villain came back the next volume.
Post Battle Wake Up
During a battle or other large-scale event, the MC kills the Big Bad or activates/destroys the MacGuffin and then passes out. Suffering a loss and having to be rescued off-screen counts too. We then cut to them waking up in a bed or hospital after the battle is completely over and the other characters have to explain what happened with the mop-up or escape.
The Hobbit After Bilbo blacks out during the battle of the Five Armies he wakes up after the fact and it is explained how it ended. A similar thing happened with Frodo waking up after the one ring was destroyed.