What does D&D 5e define as a living creature? More specifically, which creature types would be considered not to be living? The only creature type I see that suggests nonliving is undead.
Page 7 MM:
Undead are once-living creatures brought to a horrifying state of undeath...
The phrase "once-living" suggests that it is no longer a living creature, but what about Constructs, Elementals, Fiends, Celestials, etc.?
The Bag of Devouring directly mentions this on page 153 DMG:
Animal or vegetable matter placed wholly in the bag is devoured and lost forever. When part of a living creature is placed in the bag, as happens when someone reaches inside it, there is a 50 percent chance that the creature is pulled inside the bag... Any creature that starts its turn inside the bag is devoured, its body destroyed.
Given the mention of "living creature" as to what the bag specifically pulls in, and the additional mention of "Any creature" suggests that there are living and unliving creatures.