fix(mcp-sync): route tests never follow COPILOT_HOME, and docs name Copilot (#581)

The route test cleared only the registry CLIs' relocation vars, so with
COPILOT_HOME exported it wrote its fixture into that real Copilot config.
It now clears the sync-only tools' vars too, and Copilot's install probe goes
through the test's own installed set instead of the machine's PATH.

Docs: CLAUDE.md, the API reference and the Settings reference name COPILOT_HOME
and the sync-only table; a missing comma in docs/cli-registry.md; the
mcp-sync.ts overview and the Sync confirm mention Copilot.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

CLAUDE.md

@@ -248,7 +248,7 @@ Codeman is a Claude Code session manager with web interface and autonomous Ralph
 
 ⚠️ **llama-swap endpoints** (one model at a time): the apply routes check `GET /running` and return `requiresConfirmation` before evicting a model another live session uses; `confirmedSwap` and `confirmedContext` are SEPARATE flags and must stay so. Claude alone gets a context floor (`CLAUDE_MIN_SAFE_CONTEXT_TOKENS`); context is parsed from `/running`'s `cmd`, never trusted from `/props`. Backend log lines come from llama-swap's `/api/events` `upstream` source, never `/logs`. → [architecture-invariants#custom-model-endpoint-profiles](docs/architecture-invariants.md#custom-model-endpoint-profiles)
 
-**MCP server sync** (opt-in, `mcpSyncEnabled`, SYNCED, default OFF; `src/mcp-sync.ts`, `GET`/`POST /api/mcp-sync`): copies each installed, enabled CLI's user-level MCP servers into the others. It is the ONE subsystem that writes another CLI's REAL user config (`~/.claude.json`, `~/.codex/config.toml`, `~/.gemini/*`, opencode's), which is why it is opt-in and admin-only in multi-user mode (both verbs 403 for a non-admin, and the Settings group is hidden for them). Where each CLI keeps the file is registry data, `capabilities.mcpConfig` (`{ path, format, relocation? }`), never a branch on the id. ⚠️ ADDITIVE only: a name already defined, in any shape, is never edited or removed (a different same-name definition is a reported conflict), and a server switched off in its own CLI is never copied. ⚠️ Never write a file that did not parse; re-parse the NEW text and require every added server to read back before the tmp+rename (written through a symlink, previous file kept as `<file>.codeman-bak`, one apply at a time, else 409). ⚠️ A file that receives copied `env`/`headers` (secrets) is left `0600`, and so is the backup. ⚠️ Responses carry server NAMES only, never env values, headers or file text: a parse failure is reported by line and column (`describeMcpSyncError`), never the parser's own message (smol-toml and V8 both quote source). ⚠️ `mcpConfig.relocation` names the env var the CLI reads to move its file (`CLAUDE_CONFIG_DIR`, `CODEX_HOME`, `XDG_CONFIG_HOME`, `GEMINI_CLI_HOME`), resolved from the SERVER env at call time; a relative value reports the target `skipped`, never a guessed write, and a per-session `envOverrides` relocation is not followed. Tests must pass `home` (which drops the `process.env` default) or clear those vars first. → `docs/cli-registry.md` (MCP server sync), `docs/api-reference.md`, `docs/wiki/Settings-Reference.md`
+**MCP server sync** (opt-in, `mcpSyncEnabled`, SYNCED, default OFF; `src/mcp-sync.ts`, `GET`/`POST /api/mcp-sync`): copies each installed, enabled CLI's user-level MCP servers into the others. It is the ONE subsystem that writes another CLI's REAL user config (`~/.claude.json`, `~/.codex/config.toml`, `~/.gemini/*`, opencode's), which is why it is opt-in and admin-only in multi-user mode (both verbs 403 for a non-admin, and the Settings group is hidden for them). Where each CLI keeps the file is registry data, `capabilities.mcpConfig` (`{ path, format, relocation? }`), never a branch on the id. ⚠️ Tools that sync but are not run modes (GitHub Copilot CLI, the first) are plain data in `MCP_SYNC_ONLY_TOOLS` (`src/mcp-sync-targets.ts`), take part only when installed or already configured, and their companion `settings.json` (`disabledMcpServers`) is read, never written; a test must clear their relocation vars too. ⚠️ ADDITIVE only: a name already defined, in any shape, is never edited or removed (a different same-name definition is a reported conflict), and a server switched off in its own CLI is never copied. ⚠️ Never write a file that did not parse; re-parse the NEW text and require every added server to read back before the tmp+rename (written through a symlink, previous file kept as `<file>.codeman-bak`, one apply at a time, else 409). ⚠️ A file that receives copied `env`/`headers` (secrets) is left `0600`, and so is the backup. ⚠️ Responses carry server NAMES only, never env values, headers or file text: a parse failure is reported by line and column (`describeMcpSyncError`), never the parser's own message (smol-toml and V8 both quote source). ⚠️ `mcpConfig.relocation` names the env var the CLI reads to move its file (`CLAUDE_CONFIG_DIR`, `CODEX_HOME`, `XDG_CONFIG_HOME`, `GEMINI_CLI_HOME`, and `COPILOT_HOME` for Copilot), resolved from the SERVER env at call time; a relative value reports the target `skipped`, never a guessed write, and a per-session `envOverrides` relocation is not followed. Tests must pass `home` (which drops the `process.env` default) or clear those vars first. → `docs/cli-registry.md` (MCP server sync), `docs/api-reference.md`, `docs/wiki/Settings-Reference.md`
 
 **Run launch synchronization**: the Run entrypoint holds an in-flight lock and disables `#runBtn` for the whole launch (≥500ms) so a double click cannot create duplicate `w<n>-<case>` sessions; `_ensureCreatedSessionVisible()` runs before `selectSession()` and `_onSessionCreated()` stays an idempotent upsert, so POST-first and SSE-first both render exactly one tab. ⚠️ **Closing has the mirror-image race**: `closeSession()` must read `wasActive` BEFORE its `await` and announce the delete via `_closingSessions`, and `_onSessionDeleted` skips the active-session handoff for ids in that set; never read `activeSessionId` after the fact. The fallback picks the first `sessionOrder` entry still in `sessions`. Tests: `test/session-close-fallback.test.ts`. → [architecture-invariants#run-launch-synchronization](docs/architecture-invariants.md#run-launch-synchronization)