Unify search panel results-mode behavior: typing should re-enter input mode on both backends

[JDonaghy]

Summary

In the TUI, typing a printable character while in search results mode (navigating with j/k) automatically switches back to input mode and appends the character to the query. In GTK, the same keypress is ignored — the user must click the query field to re-enter input mode.

Expected behavior

Both backends should behave the same. The TUI behavior (typing re-enters input mode) matches VS Code's search panel UX and is more ergonomic.

What needs to change

• Move the "printable char in results mode → re-enter input mode" logic into the engine (e.g. a new handle_search_results_key() method or extend handle_search_input_key())
• GTK should call the same method so the behavior is unified
• The char should be inserted via search_input_insert_char() (not .push()) to respect caret position

Context

Found during #311 (search panel cursor movement). The TUI path at tui_main/mod.rs:~2477 directly manipulates engine state. GTK has no equivalent path.

Priority

Low — UX polish for cross-backend consistency.