When using the browser on macOS, opening a new tab in windowed mode (which is the default mode the browser starts in) does not automatically focus on the search bar. This requires the user to manually click on the search bar in order to type. However, when the browser is switched to fullscreen mode, opening a new tab does auto-select the search bar, allowing immediate typing.

Steps to Reproduce:

1. Open Ladybird Browser on macOS.
2. Ensure the browser is in windowed mode (not fullscreen).
3. Open a new tab.
4. Attempt to type in the search bar.

Expected Behavior:
The search bar should automatically be selected when a new tab is opened, allowing immediate typing without needing to manually click the search bar.

Actual Behavior:
In windowed mode, the search bar is not selected automatically, and the user must manually click into the search bar to begin typing. This behavior does not occur in fullscreen mode, where the search bar is auto-selected as expected.

Operating System:
macOS 14.6.1 (23G93)

Browser Chrome:
AppKit

I would like to try and fix this bug myself, however I am not sure of my skills so any support in pointing me in the right direction is appreciated.