Bluetooth on iMac and iPhone won't connect with each other

The Mac and the iPhone do not “pair” via Bluetooth in the typical sense. The features that the devices can take advantage of only require that Bluetooth be turned on and also that the same Apple ID is used on each device.

iCloud sync is leveraged by the Apple ID connection to the Internet. iPhone and iPad sync to the Mac can be done wirelessly or with a USB connection to the computer.

I don't know if messages can be recovered from the Mac using USB sync.

I typically use iCloud to keep my messages synced between my iPhone and a couple Macs, and from time to time do delete messages from one or the other. When I do that, however, the other cloud sync'd device(s) may not reflect that some messages have been deleted, so old messages remain until I address them on each device. I can't say that a USB sync will put fresh copies of those old messages back on the iPhone, perhaps because I don't often sync anything but music via USB. Maybe I'm weird?

Perhaps I can point you in the direction of message recovery with these Apple documents. For up to 30 days you can recover deleted messages in the Messages app itself.

• Recover deleted messages on iPhone - Apple Support

• Messages User Guide for Mac - Apple Support

You didn't say which elderly iMac and iPhone you use, nor which macOS and iOS version and I suspect there is potential for older hardware and software to not play well with these features, but I'll keep 🤞🏽 for you. This also: 🍀