connecting iPhone to my iMac

I am having a problem getting my iPhone to connect to my iMac.

The iPhone is OS 13.7 and the iMac is OS 10.13.6 that is running on "21.5 inch mid 2011" hardware.

When I connect the iPhone to the iMac a window appears on the iPhone with a "code number" that asks

if you want to pair it with the iMac. the same code number shows up on the iMac. tapping on the question that is on the iPhone then displays a bluetooth window on the iMac showing the iPhone however it also shows the iPhone is not connected. Clicking on the line that contains the iPhone in the bluetooth display a "sub window" comes up that has "connect" displayed . Clicking on that line does not connect the iPhone. Also in the bluetooth window displays lines for the mouse and keyboard and below them each line is the word "connected".

So I have the problem of my iMac seeing the iPhone but not being able to connect to it. Apple support

was unable to help and suggested I take my iMac to a repair place to diagnose the problem.

Other facts are (1) iPhone was connected on a wire directly to a USB port on the back of the iMac, (2) connecting flash drives and other devices to the iMac all work with no problems.

Do not know what to do.

Richard