I have just added a setting to Scout that allows customizing the minimum character count in javascript, I didn't realize that was missing and limiting the possibilities.
The javascript character count limit is actually only for the suggestion dropdown, it doesn't affect the complete search result page. The reason for the javascript minimum is actually just to avoid making requests when the app knows that MySQL will not return results for less than 3 characters, as that would just waste server resources and bandwidth for empty responses.
As has been discussed elsewhere, the 3 character minimum is a MySQL setting, it's not hard-coded in Flarum backend. I believe it can be changed at the database level but might have an impact on performance.