Make sure you install Firefox properly and that you do not launch Firefox from the DMG (Disk Image) file.

Open the Firefox Disk Image file and drag the Firefox application to the Applications folder on your hard drive. You shouldn't double-click the Firefox application to run it from the Disk Image, but instead drag it out of the DMG folder.

• https://support.mozilla.org/en-US/kb/install-firefox-mac

Sorry, that didn't work. I forgot to mention that hovering the mouse over the second Firefox icon in the dock, the one with the macbook screen in the upper right corner, displays: "Firefox from Laptop." Even if my Firefox app is closed. Again, when I click on it, it displays the website from the macbook's Safari page.

I have the same problem, which appears to be a huge security flaw on recent Mac operating systems running Firefox. I noticed the Firefox icon with the tv screen after I started running Monterey (I had been running Mojave). When my wife turns on her computer (running Mojave) with Firefox, I get the extra icon. When she turns it off, the icon goes away. Then I checked and turned on Firefox on my iPhone and the Firefox icon with the tv appeared again. This time when I rolled over the icon it said “Firefox from iPhone.” When I turn off Firefox on the iPhone, the icon goes away.

Here’s the scary part: when I click on the Firefox icon with the TV screen the web page open on the other Mac computer, or iPhone, shows up on my MacBook Pro, replacing my Firefox screen.

(To agarratt) I posted a reply to your question in the thread you started here: https://support.mozilla.org/en-US/questions/1361176#answer-1466988