I assume you have been using the screen described in the following article to try to set the shortcut and it hasn't worked: Manage extension shortcuts in Firefox.

I don't think you can use \ in a keyboard shortcut for an extension function -- I assume you are limited to the same keys extension developers can choose from:

https://developer.mozilla.org/docs/Mozilla/Add-ons/WebExtensions/manifest.json/commands#Shortcut_values

Maybe one of the others will be an acceptable choice?

One possible workaround is to use an external hotkey program that translates the keystrokes from

Ctrl+\

to whatever you define in Firefox. Not sure whether that would work.

Thanks for you help and recommendation. I'll suck it up and learn a new shortcut :)