Should I turn off Bluetooth on my iMac with wireless attachments?

It's not a good idea unless you already have wired input devices on hand as jeffreythefrog mentioned. I believe certain Macs and macOS versions will helpfully warn you about that fact if you attempt to turn BT off, although I am not certain your iMac Pro or Monterey are recent enough.

If you are experiencing BT connection problems Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support is a good place to start troubleshooting.

Addendum:

As my distant cousin, jefferythefrog, said if you turn off BT your iMac is useless unless you have a cable keyboard and mouse. The Magic keyboard can be used with its charging cable but the mouse can not. The wireless Mouse Track may be used with its charging cable but not having one I don't know.

Also if or after you're running the latest version of Ventura boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists.  Reboot normally and text again.

Note:  if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode.  This makes it act as a wired keyboard as will assure a successful boot into Safe Mode.

OT 

Is you 2017 iMac the iMac Pro listed in your bio? If it is it can't be running 12.3.

If your 2017 iMac is not running the latest version of Ventura you should upgrade it to that and test again.

Also if you've install and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac your should uninstall them according to the developer's instructions and then use the free  Use the shareware app Find Any File to search for any files with a particular file name.  For XXXX software you'd do the following search(es): 

1 - Name contains XXXX

Any files that are found can be Option dragged from the search results window to the Desktop to get a copy of the file.

FAF can search areas that Spotlight can't like invisible folders, system folders and packages.  

Note: the only VPN app you should have is one that is required to access your employer's, banks or school's servers.

only if you have a wired keyboard and mouse so you can troubleshoot your BT issue. once BT Is off, then obviously the wireless keyboard and mouse will be useless in reconnecting to the Mac.

jeffreythefrog wrote:

OldToad wrote:

Is you 2017 iMac the iMac Pro listed in your bio? If it is it can't be running 12.3.

is that a typo? because both the 2017 iMac Pro, and the regular iMacs from 2017 model year can certainly run macOS Monterey.

Not a type, but a mis-read of info on the 2017. Still you should upgrade to Ventura and test the problem. Also try Safe Mode boot a try.

OldToad wrote:

Is you 2017 iMac the iMac Pro listed in your bio? If it is it can't be running 12.3.

is that a typo? because both the 2017 iMac Pro, and the regular iMacs from 2017 model year can certainly run macOS Monterey.