You contact the company and offer to pay them hundreds of millions of dollars a year (see Google and Safari and Firefox).

Smaller browsers (if they at all exist) will default to Google because that's what users expect. Except Edge. Edge will stick to Bing.

We don't even know. It's not made public anywhere :( Hence our extension requirement for the time being.

At least Chromium-based browsers have 5 second extension install/uninstall options whereas in Safari it's several minutes and so many clicks, we didn't even bother trying to build the extension.