My iPhone tries to connect to e.crashlytics.com several hundred times a day (and this is just the time it is connect to my wifi), according to my Pi-hole.
How can I identify the app that tries to establish this connection?
Crashlytics is a service to collect crash data. It is part of googles firebase service. Depending on ones views on privacy this is or is not necessarily a bad thing. It is used by lots and lots of apps. You can try to enable developer mode for the iPhone and access the logs on the device. "Guestimating" right now I would say, that a good two digit percent amount of your apps will use firebase and crashlytics, so it is hard to give an answer without a network dump or logs.