fix(mission): size backend-started forks and log launch widths

[yicheng47]

Two determined fixes plus diagnostic logging for the launch-resume width thread (#366).

#367 — MCP-started missions fork slots at 80×24, first slot visit purges scrollback

• AppState.mission_grid_hint caches the frontend's most recent known-good mission pane grid, pushed via the new mission_grid_hint_set command: once per launch after the window-geometry settle gate (unconditionally — not gated on resume-on-launch), on every workspace measurement (reset / resume-all), and on every real slot-terminal geometry push (new onSizePushed callback threaded through SlotPtyPane).
• mission_start_impl_with_size and mission_reset_impl consume the hint when the caller passes no size (the MCP reset tool had the identical hardcoded-None defect), falling to DEFAULT_PTY_SIZE only when no hint was ever recorded. The cols-gate purge itself is untouched — it remains correct for genuinely stale-width bytes (impl 0020 / feat: headless terminal model for durable session scrollback #306).
• Tests: mission_fork_size resolver triple, register-level default, and two seam tests driving resolver output through register_mission_session + complete_mission_session_spawn asserting the actually-forked SpawnSpec.initial_size.

#371 — shellContentBox falls back to full-window width and can read the wrong <main>

• Returns null on failed measurement (never window.innerWidth, which includes the sidebar); null propagates through missionPaneAreaBox / chatPaneAreaBox / estimateMissionTerminalGrid and launchDimsFor so the persisted rung takes over.
• Scoped to main[data-shell-main] (stamped on AppShell's <main>), immune to SettingsPage's second <main> under the takeover.
• Tests: missing/zero-rect main abstention, decoy-<main> selection, null propagation.

#366 — instrumentation (mechanism still undetermined; one production repro should answer it)

All info-level so it reaches the packaged build's rotating file log:

• Backend: one line per fork after successful runtime.spawn (resume / resume-on-launch / mission slots) with session, runtime, cols×rows, and size source; cols-gate purge lines with old→new cols.
• Frontend: minimal frontend_log command routes [launch-dims] lines into the same file — settle outcome + elapsed ms per launch, per-resumed-session rung detail (main rect, rail/panel widths, pane share, resulting grid), and first-fit for launch-resumed sessions only (launchResumeTrace mark/consume).

Docs

Duplicate impl number resolved: 0036-launch-resume-fork-width.md → 0038 (git mv), all in-repo references updated; 0036-trae-runtime.md keeps its number.

Verification

cargo test --workspace (556 across suites), cargo fmt --check, cargo clippy --workspace, tsc --noEmit, eslint, vitest 248/248. Peer-reviewed working-tree diff — clean review, plus dev-build smoke: settle/hint/rung/fork/first-fit/purge lines all present and cross-correlated in runner.log.

Closes #367. Closes #371. Refs #366.

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