[Bug]: Search bar cursor control is broken with physical keyboard

### Is there an existing issue for this?

- [X] I have searched the existing issues

### Is there a StackOverflow question about this issue?

- [X] I have searched StackOverflow

### What happened?

Internal user reported several issues with moving the cursor in the search bar while using a physical keyboard.

- [ ] `Left` key moves focus to the back arrow icon button. (`Right` key seems to work fine.)
- [ ] `Ctrl+Left` sometimes does not move the caret back one word. (`Ctrl+Right` seems to work fine.)
- [ ] `Alt+Left` and `Alt+Right` do not move the caret to the start/end of the line.
- [ ] `Alt+Left` sometimes moves the caret one character left and sometimes moves focus to the back arrow icon button.
- [ ] `Alt+Right` moves the caret one character right.

### Relevant logcat output

_No response_

### Code of Conduct

- [X] I agree to follow this project's Code of Conduct

No source files, tests, or entry points are named. Reproduce the listed Left, Ctrl+Left, Alt+Left, and Alt+Right behaviors in the search bar with a physical keyboard, then locate the search UI and its focus or key-handling path; done means each shortcut moves the caret correctly without shifting focus unexpectedly.

Written by the indexing model from the issue text.