### Motivation
- Interrupting a running turn (Ctrl+C / Esc) currently also terminates
long‑running background shells, which is surprising for workflows like
local dev servers or file watchers.
- The existing cleanup command name was confusing; callers expect an
explicit command to stop background terminals rather than a UI clear
action.
- Make background‑shell termination explicit and surface a clearer
command name while preserving backward compatibility.
### Description
- Renamed the background‑terminal cleanup slash command from `Clean`
(`/clean`) to `Stop` (`/stop`) and kept `clean` as an alias in the
command parsing/visibility layer, updated the user descriptions and
command popup wiring accordingly.
- Updated the unified‑exec footer text and snapshots to point to `/stop`
(and trimmed corresponding snapshot output to match the new label).
- Changed interrupt behavior so `Op::Interrupt` (Ctrl+C / Esc interrupt)
no longer closes or clears tracked unified exec / background terminal
processes in the TUI or core cleanup path; background shells are now
preserved after an interrupt.
- Updated protocol/docs to clarify that `turn/interrupt` (or
`Op::Interrupt`) interrupts the active turn but does not terminate
background terminals, and that `thread/backgroundTerminals/clean` is the
explicit API to stop those shells.
- Updated unit/integration tests and insta snapshots in the TUI and core
unified‑exec suites to reflect the new semantics and command name.
### Testing
- Ran formatting with `just fmt` in `codex-rs` (succeeded).
- Ran `cargo test -p codex-protocol` (succeeded).
- Attempted `cargo test -p codex-tui` but the build could not complete
in this environment due to a native build dependency that requires
`libcap` development headers (the `codex-linux-sandbox` vendored build
step); install `libcap-dev` / make `libcap.pc` available in
`PKG_CONFIG_PATH` to run the TUI test suite locally.
- Updated and accepted the affected `insta` snapshots for the TUI
changes so visual diffs reflect the new `/stop` wording and preserved
interrupt behavior.
------
[Codex
Task](https://chatgpt.com/codex/tasks/task_i_69b39c44b6dc8323bd133ae206310fae)
ba463a9dc7