Firefox does not “send” it, fingerprinting is done by tagging your hardware configuration from various values and create a unique key from that - independent of being logged in or any cookies - which can be used to track you. Things like browser & device user agent, browser window size, feature support (to determine browser version), etc. All of which are passively gathered by anything you could send a request to. There are ways to reduce this that Firefox and others do (such as reducing unique values in user agent, etc) but they’re not opting in to some privacy invading reporting mechanism.
Subscribed and helping fund! Good luck. You guys deserve it. Hope you meet your goal.