Sounds more like a Youtube issue then anything related to Firefox browser since you stated it happens on YouTube then that would be a YT issue to fix.

Thank you for replying, but I don't fully understand your meaning; this is occuring inside the firefox browser, inside of the search bar. If you mean that somehow when firefox goes to a youtube page, somehow youtube overpowers firefox settings and forces firefox to display the option to suggest adding youtube to search inside the firefox search bar, that very much seems like a feature that ultimately depends on firefox permissions.

I appreciate your help and I hope others will also join in.

the search bar has a little green plus circle on the magnifying glass in the search bar, and then offers to "add search engine youtube" to my search engines.

This means you are on a site that offers an OpenSearch search engine https://support.mozilla.org/en-US/kb/add-or-remove-search-engine-firefox

Not sure if that can be removed? . a glance in about:config filter for search did not seem to have a preference related to this?

Thank you for helping me understand what it is and how it works; I did not see anything in the article on how to remove it, and I don't know enough about how to use about:config to do anything.

It's pretty disappointing, I would prefer to have layout control and search bar control and not have other sites make unwanted offerings.

I do appreciate everyone helping me understand. I'll leave this question open for a few more days in case someone has a guide on how to stop it from happening.

Ok, it seems no one else has a solution. Thank you for the people who helped out, and I guess this is just how it is now. Hopefully firefox puts in something that allows this to be adjusted. I can't seem to close the topic without marking it as solved, so I guess the thread will remain like this; thank you to all again.