You cannot connect an iPhone to a Mac directly over bluetooth. You also don't use bluetooth for backups at all.
To back it up, you do so through USB cable or Wi-Fi if you have set that up previously.
What happens when you connect the iPhone to the Mac using a USB or USB-C cable?
Are you using a Lightning to USB-C cable? If so, is it rated for data transfer? Or only power delivery?
Are you using an adapter for hub?
Does the Mac not ask you to trust the iPhone when you plug it in?
Is the iPhone turned on and unlocked?