pairing iPhone 13pro with iMac
how do I get my iPhone 13pro to stay paired (connected) to my iMac?
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An iPhone will not pair via Bluetooth to a computer (Mac or Windows) or an iPad except for personal hotspot and then only if your cellular plan supports it. See the following for more information: Bluetooth: Why can't I pair my iPhone or … - Apple Community
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: Use Continuity to connect your Mac, iPhone, iPad, iPod touch, and Apple Watch - Apple Support
Also see Share files between your Mac and Bluetooth devices - Apple Support