Focus search bar in menus that have one

Whenever I open a recipes or statistics or research menu, I want to be able to search quickly by typing the name.
Research menu already allows using CTRL+F to focus the search bar. Same should work for recipes and statistics windows.
For extra QOL, the search bar should be focused automatically when such windows is opened, so I don't even have to do that additional CTRL+F press after I already pressed F1, O or G.

I don't like the idea of the search bar being focused automatically, unless it's a toggleable option. When I press T to open the tech tree, pressing T again should close it.