my iPhone 11 Pro Max does not show up on my iMac

Your preference choices appear to be correct. How are you "connected directly?"

Review: Use the Finder to sync your iPhone, iPad, or iPod with your computer - Apple Support which states:

"Open a Finder window and connect your device to your computer using a USB cable."

Antonio Scrittorale wrote:

According to Apple that is the only way to back up an iPhone in macOS Catalina via a direct connection. Problem is my iPhone does not show up.

I understood that, and wanted to make sure that you reviewed the instructions listed in: Use the Finder to sync your iPhone, iPad, or iPod with your computer - Apple Support. Follow the link in that article, which describes trusting your device: About the 'Trust This Computer' alert on your iPhone, iPad, or iPod touch - Apple Support. I had to make sure to enter the passcode on the iPhone before the device appeared in the sidebar.

Since you apparently understand those instructions, try a Safe Mode start, which may remove some old caches, that may adversely affect your displayed options. After the Safe Mode start, restart your computer normally and reattempt to connect your iPhone.

If that is not successful, review: iPad, iPhone Won’t Detect After Update macOS Catalina for a possible solution.

You may also want to try to Download/Install macOS Catalina 10.15.3 Combo Update.

You're looking in the Finder, and I don't believe that having an iPhone show up in the Finder sidebar is an option.

You'll notice that Finder/Preferences gives you choice of which things you want to appear in the Finder window's sidebar, and the iPhone that I have hooked up via USB isn't even an option.

Does the iPhone show up when you launch iTunes?

Patrick Wheeler wrote:

You're looking in the Finder, and I don't believe that having an iPhone show up in the Finder sidebar is an option.

Yes "having an iPhone show up in the Finder sidebar" is an option using macOS Catalina.