System Preferences freezes when I go to "Security & Privacy"

First, try booting Safe Mode. This allows your Mac to check itself for issues. The way to do this is reboot and press Shift.

If that doesn't work, try running First Aid in Disk Utility.

If that doesn't work, try reinstalling macOS from the Recovery partition.

What do you mean by migrating? You can just install macOS Catalina on the USB drive and then use Migration Assistant to transfer data from your Mac to the USB with macOS Catalina. Since you are running macOS Mojave, you will need to first install macOS Mojave on the USB. Then, you can update to Catalina.

Good luck!

The Catalina updater runs a critical firmware update. The install method you describe has bypassed the firmware update. As suggested elsewhere, install Mojave on external drive, boot from the drive ( holding Option at boot time is my preferred method), and run updater.

There was also a critical firmware update with High Sierra that Apple requires for Mojave. If you managed to bypass that upgrade and went directly from Sierra to Mojave, you may want to ask a new question how to accomplish that. (One would hope the Catalina upgrade will supersede the old firmware, I can't say.)