Yup the content is supposed to control HDR,a nd the way I have it set up that is excatly what happens. I use MPC-BE, which when a HDR video is opened such as a movie or a phone camera recording where I've used HDR10, it will activate HDR mode on my monitor as the signal is sent via the MPC-BE Video Decoder:
As for games, only a handful of PC games support the sending of a HDR signal automatically and triggering the monitor to enter HDR mode. I know all of Capcom's games do this, but others you have to enable HDR before launching the game, then manually disable it once you have finished your session. Not a huge issue but having the auto trigger in all games would be ideal. Lazy development I guess so kudos to Capcom and a few others for doing it properly.
I never need or care for browser based HDR though as I rarely watch stuff that warrants HDR through a browser.
I have seen this too, it just happens intermittently and never really figured out why it happens and yeah only on Facebook so it's definitely a Facebook issue ever since they changed to the new "theme" layout, not an issue caused by Firefox.