Dock not showing on left/right side of external monitor

I selected 'displays have separate spaces' and dock hiding and the behavior is as you described - except it appears to work properly on my machine. At the bottom of the external display if I hover the mouse to the left or right I get the dock to appear (although it is a little finicky about it) and I can click on it. If I hover near the center, nothing happens.

So something peculiar to your machine is probably in play. Standard things to check include:

Does this occur for a different user, e.g., Guest? How to test an issue in another user account on your Mac.

Does this occur after starting up in Safe Mode?

Consider the possibility of a third party software conflict.  EtreCheck can be used to investigate what is installed.  You can post the report here. Someone might spot something.

The Dock should not appear on a side that is shared with another display as it appears in the Arrangement tab of Display System Preferences.

I'm not sure I quite understand what you are describing, so I could only offer what is supposed to work.

If you have one display above the other, the Dock will not appear on the top display.

If you have them side-by-side, you can only show the Dock on the outer edges of either display.

I don't think it is supposed to do that. I know it didn't in past OS, but I'm not sure about Catalina and I don't have a way to check as I don't have access to a Catalina system with multiple monitors.

I guess I still down't know what you are describing.

In Mission Control System Preferences, do you have "Displays have separate spaces" selected?

As I stated, with your displays set up like that, the Dock should not show up on the bottom edge of your upper monitor if you have it set to Bottom. It should only show up on the lower display at the bottom.

If you have it set to left or right, I think it will show up on either.

A lot of people complained about it not showing the Dock when you did something like that in past versions of the OS. Maybe Apple changed it in Catalina so that if you move to an unconnected area, it would show. I don't have a way to check on my systems at this moment.

I tried it and I can't get the dock to show on the external display.

Maybe I don't have all the same settings - do you have "Displays have separate spaces"?