I agree Firefox doesn’t have a large share of the browsers, but if you are basing it on user share then the only mainstream browsers are safari and chrome. However, the term third party is generally utilized as a fork of a primary access point or is the access point via another means, even if it’s original.
For example, the apps to access lemmy are third party as they are not created by the original devs for lemmy. In this argument FF is classified as first party not third.
Don’t get me wrong I understood what you were trying to say, but based on your reply then pretty much chrome would be the only mainstream browser.