I've used the library system to add a bunch of assets that I haven't actually purchased, in the event that I might find use for them in the future, or they happen to go on sale.

Is there a method of seeing the current price and whether they are on sale within the library? Also, which ones you actually own?

Additionally, are there any email notification systems? Like Steam's emailing when an item in your wishlist goes on sale? Or, a watch list on new assets with certain tags being added to the store?

OK. So, it would appear that I do get notification for sale items. Obviously I missed that.

Is there a way to see which items in your library you own (aside from the "owned" list)? And perhaps a price, and whether it's currently discounted? Maybe I'm just not using the system correctly...

This page will list everything in your collections or from your followers that is on sale: https://itch.io/library/things-on-sale

There's current no way to filter your library to remove things you already own or vice versa.