Summary:

- Preserve spinner/logo prefixes from live terminal titles when terminal
threads have custom titles.
- Store raw terminal titles and custom user titles separately,
recomposing display titles on demand.
- Keep spinner prefixes out of the title editor while preserving
sidebar/search display behavior.

Tests:

- cargo test -p agent_ui
test_terminal_custom_title_recomposes_with_live_spinner -- --nocapture
- cargo test -p agent_ui
test_terminal_title_editor_excludes_spinner_prefix -- --nocapture
- cargo test -p sidebar
test_agent_panel_terminals_appear_in_sidebar_and_search -- --nocapture

Closes AI-304

Release Notes:

- Fixed terminal thread titles to preserve animated spinner and logo
prefixes after renaming.