Since we had the issue the foxyproxy installed from packages.debian.org did not work, we can be pretty sure that Tor Browser does add-on signature checking just like Firefox. (xpinstall.signatures.required)
Our trouble of installing add-ons from addons.mozilla.org is most likely not related to xpinstall.signatures.required. An add-on would either never be listed in Firefox's add-on manager or labeled as deactivated due to failed signature check.
I speculate, that Tor Browser is doing something to prevent users from the installation of add-ons which we can hopefully disable.