No. Firefox always randomizes the extension ID used for URLs to web accessible resources on each restart [1]. Apparently, manifest v3 extensions on Chromium can now opt into similar behavior [2].
[1]: https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/Web...
[2]: https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/Web...
An additional improvement added in manifest v3 in both Chromium and Firefox is that extensions can choose to expose web accessible resources to only certain websites. Previously, exposing a web accessible resource always made that resource accessible to all websites.
That's a different form of defense. The original claim in this thread was that LinkedIn's fingerprinting implementation was making cross-site requests to Chrome Web Store, and that they were reading back the response of those requests.
Firefox isn't susceptible to that, because that's not how Firefox and addons.mozilla.org work. Chrome, as it turns out, isn't susceptible to it, either, because that's also not how Chrome and the Chrome Web Store work. (And that's not what LinkedIn's fingerprinting technique does.)
(Those randomized IDs for content-accessible resources, however, do explain why the technique that LinkedIn actually uses is is a non-starter for Firefox.)