When using JAWS, users are unable to use the arrows to read results in the dropdown

Thanks a lot for reporting this!
However, I fear I’m not very good at frontend development in general, and have no idea how this could be fixed. Is this only broken for search autocomplete, or also for other autocomplete fields in Drupal (e.g., selecting taxonomy terms for new content)? We mostly just use the autocomplete functionality from Core, so this might be a general problem in Drupal.
Anyways, I’d be glad if someone would have some suggestions for a solution.

I think you meant to move it to Drupal Core?