Error output:
JavaScript error: chrome://messenger/content/mailCommon.js, line 171: TypeError: can't access property "startsWith", window.gMessageURI is undefined

There are multiple issues here.

The variable gMessageURI is set in aboutMessage.js, which means it is never set, when the message pane is disabled.
https://searchfox.org/comm-central/rev/5ecdae89921e4af3ed68a4b96ede25f6bc1c0e0c/mail/base/content/aboutMessage.js#112

Furthermore, the context click does not the select the message. Even if the message pane is enabled, the copy command tries to copy the last selected message, not the message we context-clicked on. (I think a context click should select the message)

The copy command is looking for gMessageURI on the window object of the message list and does not see it, because it is defined on the window of the message pane.

If this isn't supernova related, please obliterate my changes

Bug 1815619 fixed part of it at least.

John, is this still happening?
Could you provide a bit more info on an STR, as well as the location of the "Copy Message" in context menu?

It has been fixed elsewhere \o/.

Edit: It was the "copy to" context menu of the thread pane. Sorry for being sloppy in the bug title.