It really looks to me (a non-lawyer, non-legal-expert) as if the "oh we just need the rights necessary to fulfill the requests you make to Firefox" terms are kind of trying to confuse Mozilla-the-organization with Firefox-the-software-running-on-your-computer. Like, they seem to be saying that if you e.g. submit some text to a comment box on some website, then in order for Firefox, i.e. the copy of Firefox running on your computer, to send that text to that server, it is necessary for you to grant Mozilla, an organization that does not own your computer and whose computers are not running your copy of Firefox, all the rights necessary for them to send your data to the requested server.
It's as if they're trying to say that the copy of Firefox on your computer is considered to be part of and acting on behalf of the Mozilla organization and therefore anything it does, even actions directly requested by you like loading a page when you click a link, are legally the actions of Mozilla and not you. Which doesn't make any sense to me. Like, if a user uses Firefox to do something illegal is Mozilla then liable for that? If I go into my file manager and make a copy of a file whose contents I own the copyright to, do the makers of the file manager and of the filesystem and of every other piece of software in the chain all need to be granted the legal rights to make copies of my content, just to protect against me turning around and suing them for copyright infringement over the copy I myself instructed the file manager to make? That seems completely bonkers.
My understanding is that websites have this sort of language in their ToU because once you submit a comment / post / whatever to be displayed publicly, it is necessary for software running on their server and under their control to then transmit copies of your content whenever someone loads the page. But when you operate Firefox as a web browser to access a (non-Mozilla-owned) webpage, no server owned or operated by Mozilla should be involved in the process unless you have explicitly opted into telemetry, data sharing, VPN/proxy services from Mozilla, etc.