Browsers nowadays use their address bar not only for entering web-page addresses, but also for using search terms that should be passed to a search engine. Many years ago you first had to type the address of the search engine's website (like www.google.com) into the address bar, to get to a page where you could then type your search terms on that page. Such pages still exist, but seem to automatically transfer anything you type on them to the browser's address bar, like you were typing there.
Anyway, which search engine would be used to find things you type in the address bar that are not web addresses is usually a browser setting. On FireFox you can specify what your default search engine is. The default setting for this is google.com, which is probably why it displays the Google icon next to the address bar. But you can alter that in the FireFox settings menu.
I hit the back arrow and brave said it had a '500 Internal Error', whatever that means.
The message probably was '500 Internal Server Error'. When you get such an error it is not your browser's fault; the website you were viewing did produce the page with this error message (which your browser then correctly displays) because something went wrong on that server. In this case that doesn't tell us very much, because we cannot be sure which website we were accessing after using the back button. It could have been the website of the search machine.
Since the errors already occur when you directly type chessvariant.com addresses in the address bar, it is best not to involve any search machines.
Just out of curiosity:
I made a copy of the page souce of the CVP home page, and put that back on the site as http://chessvariants.com/home.html . Can you access that page with your iPhone?
Browsers nowadays use their address bar not only for entering web-page addresses, but also for using search terms that should be passed to a search engine. Many years ago you first had to type the address of the search engine's website (like www.google.com) into the address bar, to get to a page where you could then type your search terms on that page. Such pages still exist, but seem to automatically transfer anything you type on them to the browser's address bar, like you were typing there.
Anyway, which search engine would be used to find things you type in the address bar that are not web addresses is usually a browser setting. On FireFox you can specify what your default search engine is. The default setting for this is google.com, which is probably why it displays the Google icon next to the address bar. But you can alter that in the FireFox settings menu.
The message probably was '500 Internal Server Error'. When you get such an error it is not your browser's fault; the website you were viewing did produce the page with this error message (which your browser then correctly displays) because something went wrong on that server. In this case that doesn't tell us very much, because we cannot be sure which website we were accessing after using the back button. It could have been the website of the search machine.
Since the errors already occur when you directly type chessvariant.com addresses in the address bar, it is best not to involve any search machines.
Just out of curiosity:
I made a copy of the page souce of the CVP home page, and put that back on the site as http://chessvariants.com/home.html . Can you access that page with your iPhone?