According to Firefox, Version 78.11.0esr is the current version for Mac and was released on June 1, 2021. I checked this on both of our Macs.
First on the MB Air I opened Firefox and clicked on "About Firefox". The window that opened advised "Firefox is up to date" and that it has Version 78.11.0esr. To the right is a link "What's new". I took a screen shot of this window.
I clicked on "What's new" and a new page of Firefox ESR Release Notes opened. This advises: Version 78.11.0, first offered to ESR channel users on June 1, 2021. This is the date on which both our Macs were last updated to the CURRENT release of Firefox, less than 3 weeks ago. I took another screen shot of this.
I then scrolled down on this Release Notes page to Mac Operating Systems for this release of Firefox. It lists the following: MacOS 10.9, MacOS 10.10, MacOS 10.11, MacOS 10.12, MacOS 10.13, MacOS 10.14, MacOS 10.15 and MacOS.11. I took another screen shot showing this.
I then opened YouTube as it is one of the websites that for the past few months has opened on the iMac with "Please update your browser". As always on the MB Air, this warning did not happen. It went straight to the YouTube cookies page.
Then I checked the iMac. It has exactly the same version that Firefox released less than 3 weeks ago. On opening YouTube the "Please update your browser page" appeared. I clicked on the "Remind me later" link at the bottom and it then went to the cookies page.
All info I can find indicates that our Macs have the same current version of Firefox that was released on June 1, 2021. As far as I can see all the Preference settings are the same. Somehow the Firefox installation on the iMac is giving incorrect version info to websites. I would like to know how to correct this on the iMac. Is there a particular version ID setting in Firefox that can be changed? Firefox must be sending something about versions to websites. What is it sending and where may it be found? It just needs correcting on the iMac.