Aside from the information window with things like connections, block height, etc, etc. Is there any neat bits on Bitcoin Core to look at? Things like how many transactions my node has personally verified or anything?
I would suggest running a full node on Tor instead of clearnet, if possible.
Since you are already running full bitcoin node you can also do the same thing for mempool.space explorer, and you will get detailed information about transactions and mempool state.
This is great open source project and you can easily install it with one click or manually:
https://github.com/mempool