connecting iMac and iPhone 13 via Bluethoot is impossible. On thr iPhone a pop up says " iMac is not supported"

What are you trying to accomplish?

Macs and iPhones use Bluetooth behind the scenes, but don't pair with each other. Usually you would get a Mac and iPhone to work together through some combination of

• iCloud synchronization
• Connections to the same e-mail accounts
• Connections to third-party cloud services
• Continuity features

See also the Table of Contents in the online iPhone User Guide.

Bluetooth pairing an iPhone or iPad and a Mac is not supported. 

If you are attempting to use Handoff/Continuity or AirDrop, that does involve Bluetooth but the devices are NOT paired; Bluetooth just needs to be on and the devices in range of each other. The following may help with Handoff/Continuity issues: Continuity features and requirements for Apple devices - Apple Support

Also see Share files between your Mac and Bluetooth devices - Apple Support

And see the information in: Bluetooth: Why can't I pair my iPhone or … - Apple Community

filippo103 wrote:

That is correct, you can't pair two Apple devices via bluetooth unless you're tethering.