Discovered as part of T287500

List of steps to reproduce (step by step, including full links if applicable):

• Initialize a screen reader, like Orca. I also tested this with TalkBack on Android mobile and the behavior was mostly the same.
• Navigate to developer.wikimedia.org
• Use the screen reader to navigate to the search query box.
• Type in a search query

What happens?:

• There is no indication to the screen reader that the search results are appearing in a modal
• If the screen reader user presses enter/return after typing their query, the first page in the search results loads. This may be a page that is in a different language due to https://phabricator.wikimedia.org/T306458. There's no way for the screen reader to navigate the search results or get to anything other than the first result in the list.

What should have happened instead?:

• There should be some indication to the screen reader that the content displayed on the page has changed, and some way for the user to navigate those search results and select the one they want.

Software version (if not a Wikimedia wiki), browser information, screenshots, other information, etc.: Orca on Ubuntu 20.04.4 LTS; Chrome browser version 101.0.4951.64; TalkBack on Android 11, OnePlus 6t mobile phone, Chrome browser 102.0.5005.98