How can I disable the volume control overlay in Mojave?

Please provide more information. What bezel? Do you mean the menubar icon or something else?

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I went looking in the directory path, and found that the named item, BezelUIServer, is no longer there and neither is its directory. A deep search of the System folder did not produce the file, so it's safe to assume it's no longer in Catalina.

You cannot disable that. It is built into the OS. If you want to control the volume another way, then use the menubar item. If it isn't in the menubar, then enable it in the Sound preferences.