I'm not entirely sure that's true. The money goes to Mozilla and Mozilla will use it to fund Firefox (and other projects). It seems to work exactly how one would expect it to work - you just can't donate directly to a project such as Firefox.
There are limits to how much money they can move to projects due to their structure as a 501(c)3, (but all of their projects are towards an open web) so maybe not all of the funding goes to Firefox, but it still does go to Firefox.
I just use the ping integration of Home Assistant, simple for me since I've already got HA running.