Giga display shield with Uno R4 Wifi

Thanks!
That device uses 3.3 volt logic signals, not suitable for an UNO that uses 5 volt signal logic signals. Level shifters are needed.

I don't know the Giga WiFi R1 at all.....

Mounting to a connector..... What is the problem there?

You aim for a quite advanced setup, beyond my experience. More information will surely trigger more knowing helpers.
What's Your goal, what's this setup supposed to be used for?