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>

src/web/public/settings-ui.js

@@ -1235,7 +1235,7 @@ Object.assign(CodemanApp.prototype, {
       show('Apply or Save settings to turn MCP sync on first, then preview or sync.', 'save-first');
       return;
     }
-    if (apply && !confirm('Add missing MCP servers to every installed, enabled CLI\'s config file? Env values and headers on those servers are copied too.')) return;
+    if (apply && !confirm('Add missing MCP servers to every installed, enabled CLI\'s config file (and GitHub Copilot CLI\'s, when it is installed)? Env values and headers on those servers are copied too.')) return;
     show('Working…');
     const res = apply ? await this._apiPost('/api/mcp-sync', {}) : await this._api('/api/mcp-sync');
     let body = null;