Imac as a monitor for MBP m4

That iMac does not support Target Display Mode, and that MBP does not support using any iMac as a Target Display.

You can set that iMac up as an AirPlay Receiver for AirPlay to Mac, but this won’t use the full resolution of the iMac and is a lower quality connection method than a cabled connection to a real monitor.

Continuity features and requirements for Apple devices - Apple Support

There is also a third-party workaround product called Luna Display, but it, too, may come with compromises.

You don't.

The iMac cannot be use as a monitor for the MBP or any new Mac.

The technology that Apple used was killed off when the first Retina Macs were released in 2014 and died in software with the release of macOS 11 Big Sur.

Using an iMac as a monitor - Apple Community