If a mimic was reduced/enlarged by a spell (enlarge/reduce), would the mimic try and turn into a object to match its new size (even if it's for a minute)? For example, if I enlarged it, would it try to possibly be a small shack or outhouse?
It probably can.
Shapechanger. The mimic can use its action to polymorph into an object or back into its true, amorphous form. Its statistics are the same in each form. Any equipment it is wearing or carrying isn't transformed. It reverts to its true form if it dies.
If something changes its size, nothing in the Mimic traits restricts it to assume the form of a Medium-size object.
Since the mimic is a Medium size creature, I assume that it can only transform into an object of its same size. A Medium size creature can occupy a maximum area of 5 x 5 x 8 feet, as the rules says in the sixth page of the Monster Manual (Size Categories table) and at page 17 of the Player's Handbook (quoted below).
Characters of most races are Medium, a size category including creatures that are roughly 4 to 8 feet tall.
Further support that a larger Mimic can transform into larger objects can be found in Waterdeep: Dungeon of the Mad Mage, pages 75 & 76 (spoilers ahead):
Area 11 of Level 5 (Wyllowwood) has a Large-size mimic which is disguised in the form of rowboat, which is large enough for 4 characters.
Quote from Area 11a: "Tethered to the mouth of a narrow cave at water level is what appears to be an intact wooden rowboat that can hold up to four characters and their equipment. The boat and its tether are, in fact, a Large mimic with 67 (9d10 + 18) hit points. The mimic adheres to any creature that steps into it or grabs its "rope".
Looking back at the features of Mimic in older editions, The Ecology of the Mimic (Dragon #75) says:
The creature can, as we all know, alter the external configuration of its form at will, within the limits imposed by the actual volume of its form.
In the AD&D 2nd Edition module, The Ruins of Undermountain II: The Deep Levels, a potential enemy is the Greater Mimic, a Huge size creature that "can cover a whole room or a small building such as a tomb".
So yeah, the mimic can probably transform into a Large-size object if its size is Large.
Proving that, should it become a large object? If it is naturally large, it probably should, because it can grapple multiple prey at once. If it is temporarily transformed into a larger-size, the mimic shouldn't be able to discern if its a good or bad choice due to its low Intelligence.