Do they allow extensions on Chrome?

They do, approved extensions. But for example dark mode can be added to chrome, but not to ff.

The chrome add-on system has the ability for the management organisation to set a whitelist for your corporate computer.

I don't recall this to be the case for Firefox (that may have changed by now?). So you can only use vanilla Firefox in a corporate managed profile.

So in the org I work for, we aren't allowed to add through the normal chrome extensions process. Instead you must request the add on in an intranet app, assuming it's preapproved, and then reload your desktop applications.