Ideally it would be an option for me to turn on and off in the Setup dashboard somewhere so that if someone enters a category on the right, if they search in the search bar, it will only be for items in that category.
We will try to add this option in 2 days.
We've added an option to the Search module to search within selected category.
Open your project settings->Forum settings->Layout customization. Select the "Topic List" tab and click on search module settings. The option is "Search in the user's selected category only"