Display details stored in address book while receiving a call

True Phone Dialer & Contacts & Call Recorder is a contacts and dialer app that does pretty much what you are looking for except displaying email ID. It's free for 7 days after which you can disable ads by going pro.

Install the app, from 3 dots menu at bottom right → Incoming /Outgoing Calls → disable incoming call notification to see full screen call details.

On my OnePlus 7, Android 10,using the default contact app I filled in details and it displays event date (birthday), address & notes ( Don't be Covidiot- you can replace this by Email address if you badly need that)

(Click to enlarge)

From 3 dots menu at bottom right → Incoming /Outgoing Calls → additional info, select to show (needs to be manually edited in the contact information using this app)

(Click to enlarge)

I added job information & Nickname manually (my contacts app doesn't have those fields) and now the screen shows

(Click to enlarge)

Eyecon:caller ID, calls and phone contacts is another alternative that harvests caller information and photos from social media and displays - in case, it helps somebody who likes that approach.