iPhone 14 Pro Max not showing up in Finder on iMac

Give this a try: disconnect the iPhone from your Mac and boot into Safe Mode according to How to use safe mode on your Mac . Connect the iPhone with its charging cable and see if the Finder shows it in the sidebar. You may get this notification - I get one after every system update or upgrade:

Just select Install.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: 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 insure a successful boot into Safe Mode.

Have you restarted your Mac lately?

While you're at it, reboot the iPhone.

If a simple reboot of your Mac doesn’t fix things, see if the problem still happens in safe mode.

How to use safe mode on your Mac - Apple Support 

Safe mode will often correct weird software behavior by forcing the OS to do disk repair, clear caches and other housekeeping and temporarily disables third-party mods. When you're in safe boot, the machine won’t be at its best performance, especially with graphics, but that's expected.

Does the same thing happen while in Safe mode?

You can exit safe mode by restarting your Mac normally, then reevaluate the problem.

Safe boot steps are in the link. yes, you can chose Apple menu  > Restart. Then, as the startup chime sounds, press and hold the Shift key while the Mac boots. Will probably take a little longer than normal.

You won't lose any data. Safe mode basically shuts down third-party software at startup and runs only the OS and basic drivers.

C-M wrote:

When I shutdown and then restarted the iMac it was unchecked again! So I’m hoping that this was the issue as it has worked for me now.

Since the settings are switching back when you reboot give this a try: boot into Safe Mode according to How to use safe mode on your Mac and set the settings to what you want. Reboot normally and check the settings.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: 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 insure a successful boot into Safe Mode.

C-M

Another thing I want to bring up, is if you feel like you are spinning your wheels, just pick up the phone and call AppleCare and they can actually speak to you and even log into the phone and your iMac (assuming you permit them to) to help you through the process. If you don't know the phone number for AppleCare in your area please click AppleCare Contact Info to find it. This is an international forums so we have no idea what country you are in and of course AppleCare has coverage in every country they have a presence in.

However, again if you were using iCloud this would have been done hours ago so please consider doing that!

You really should be backing up to iCloud, this is MUCH easier than trying to backup to the iMac. The phone will not show up in Finder when connected. Please refer to:

Back up iPhone - Apple Support

See Back up iPhone - Apple Support - piece of cake.