Oh, my bad! I see the confusion. I actually mean that the two were paired/connected wirelessly through WiFi by activating their Bluetooth. I thought this method is called connecting using Bluetooth?
Anyway, this is how I was/am doing it:
On iPhone: 'Settings' > 'Bluetooth' activated, iMac appears on the My Devices list as 'Not Connected'. To connect the two, I tap iMac, but I get a message "Connection Unsuccessful. Make sure iMac is turned on and in range".
On iMac: I tap the 'Bluetooth icon' on the top right corner of the iMac (I leave it always ON) > 'Bluetooth Preferences', my iPhone is on the Devices list also with status Not Connected. So when I tap on it, nothing happens. The spinning wait cursor just keeps spinning.
Trying to solve the problem, I did a few times the 'Forget This Device' respectively removing the device from the list and pairing the two again technique. The pairing was always successful but the problem is still there. I can't get that status change from Not Connected to Connected. Again, I don't really have a particular reason at the moment why I want them to connect. I'm just curious why. My daughter instinctively remarked that my iPhone is nearing its extinction.