That is a feature that uses WebRTC to share your screen via internet.

• https://support.mozilla.org/en-US/kb/screenshare-safety
• https://webrtc.org/

• https://developer.mozilla.org/en-US/docs/Web/API/Screen_Capture_API/Using_Screen_Capture

When the permissions are manual set I have noticed they do remain if FF is restarted. For example if I go to "set cookies" to block and close the browser it returns to its original setting. Can this be made permanent?

Permissions and other settings you make for a specific website are stored in permissions.sqlite (and content-prefs.sqlite) in the Firefox profile folder as part of the Site Preferences, so if you do not keep these permissions then this clear the Site Preferences when you close Firefox. Not all permissions are saved and some may only apply to the current session.

In case you use "Clear history when Firefox closes" or otherwise clear history.

• do not clear the Site Preferences

• Options/Preferences -> Privacy & Security
  Firefox will: "Use custom settings for history":
  [X] "Clear history when Firefox closes" -> Settings
• https://support.mozilla.org/en-US/kb/delete-browsing-search-download-history-firefox

• clearing "Site Preferences" clears exceptions for cookies, images, pop-up windows, and software installation and exceptions for passwords and other website specific data
• clearing "Cookies" will remove all selected cookies including cookies with an allow exception you may want to keep

I am not able to find the cause of the permissions defaulting after closing and opening FF. Why wouldprmisions be dependent on cookies and site preferences?

The permissions do not rely on cookies, but they are part of site preferences because you set this permission for a specific domain (origin).

Are you removing the Site Preferences ?

My FF is set to private mode. Yet each domain can be set with permissions but it will not maintain those permissions when restarted.

When you are in PB mode then permissions work the same as in regular mode, but since all data is kept in memory and not written to the profile folder, you won't keep permissions set in PB mode. I think that you keep block exceptions for cookies and passwords and maybe some other exceptions, but screen sharing doesn't seem to be included judging from your experience.

If I have several domains set up with specific permissions it seems ridiculous to reconfigure all the domains permissions after FF is restarted. This must be a over sight

Using Private Browsing mode means that you do not want to keep any history references across a session stored in the profile folder and that includes website specific permissions. Site specific permissions are stored with the domain in clear text in permissions.sqlite and content-prefs.sqlite and that wouldn't be private. If you want some partial PB mode that allows to keep things like site preferences then use regular mode and use builtin means (Clear history when Firefox closes) to clear data like browsing history and cookies if that you do not want to keep.

That does not seem reasonable. the items that are cleared when using Private mode are not in my control but are done by the web site. Permissions are in the users control and when set are displayed in the URL box for user to know they are active. I do not think having the permissions reset when FF closes is reasonable action.