Connect M1 Mac Mini to Macbook Pro

Nope' a cabled display connection will not work with those Mac's. Unfortunately that function was dropped yeas ago by Apple and neither of those Mac's support Target Display Mode.

see > https://support.apple.com/en-us/HT204592

You can use Screen Sharing and File Sharing between the MacBook Pro and Mac Mini over your local network or Ethernet, but it takes an external display to get the Mac Mini setup and connected.

see > https://support.apple.com/guide/mac-help/turn-screen-sharing-on-or-off-mh11848/mac

and > https://support.apple.com/guide/mac-help/set-up-file-sharing-on-mac-mh17131/mac

You're welcome.

Yes you will need to get and use an external display with the Mac Mini.