I suppose it doesn't matter how you leave Schengen. But this forum is about the use of Eurail/Interrail passes, not about Schengen regulation details.

90 days MAX is for having NO visa.

You need a real VISA (=not that card, but an extra stamp in your passpt) when you want to stay longer.

Your passpt will be checked+registrated-(of course since this century its all automatic and stored in the giant system) on enrty and leave of the combined Schengen zone. Overstay: hard to say what will then happen, but what you can be sure of is that you will be BANned from entry for some period-even for just changing planes on the way back to USA if you use some EUR-airline and have to change planes inside the zone.

And yes-use a general touristy forum for all the strange and looking for the finest detail of USA thinkers-all of them will allready have been tried out and tested+answered before!

If you stay more than 90days in the Schengenarea it can be cause major Problems like a entry ban for a specific period. The bestway is to have route in mind with Countries that are not in the Schengenarea For example UK, Croatia,Serbia,Albania,Montengro,Turkey and in less stressfull times even Ukraine or Moldova.
All informations regarding Schengen can be found here https://www.schengenvisainfo.com/

Thank you everyone for your helpful responses @rvdborgt @mcadv @seewulf ! I do plan on taking Eurail and mixing up the route to maximize the trip without overstaying whether that be Schengen or non Schengen. This was an especially great suggestion! @seewulf . Will look more into it!