I really like your idea and I think it would be fun to play. One thing I would caution you on is being sure to balance the loot randomness. Game Maker's Toolkit has a great video on "Two types of randomness" that I would highly recommend watching to get some inspiration.

Seeing as my last game in a game jam was about being a crow stealing nuts from squirrels I can't not rate this one. Ok so things you might consider. Not sure where you live but where I do there are three types of squirrels. Fox squirrels are big derpy and gentle. They are adorable, clumsy, and definitely not "with it" I honestly love them but I have no idea how they survive. Red squirrels are small, passive, and wicked fast, think Piglet, but as a squirrel. Then there are Grey squirrels, they are the rogues of the squirrel world, they push around red squirrels, take their stuff, and will readily throw down with other grey squirrels over nothin. They are resourceful medium built and will readily shout at you if you are on their turf, from a distance of course. What type of squirrel do you want your Main Character to be. He sounds like a fox squirrel to me, which would be the most fun honestly, but that may not be everyone's impression of a squirrel is what I am getting at, so be sure to differentiate your MC somehow early on.

Next, I love the concept of having good stuff vs junk stuff. You might consider rethinking Noggins. Especially if you want to make your MC a derpy squirrel. See there is an opportunity here. If you wanted to you could have the player know something about Noggins that your MC doesn't. If you have your MC telling the player and everyone else he thinks Noggins is doing this just to be mean, he's imposing capitalism, a villian, a complete jerk who steals nuts etc. BUT then you have the "good" items Noggins wants be litter... he wants bottles and trash bags, smashed juice boxes, and in general all the trash that humans junk up the park with... He doesn't want people's phones, their jewelry, their wallets... All of the sudden Noggins is a very different character to the player... and your squirrel has no idea. To your MC squirrel Noggins is the villian, he took the nuts. But to the player he's training squirrels to help cleaning up the park. Then the more your MC complains about Noggins he looks like he doesn't get it Noggins is totally playing him, and it is much more interesting.  It makes Noggins both the villian and a "good guy (kind of)." It would be one heck of a twist.