feat: make Antigravity a first-class CLI across docs, installer and UI

Antigravity (agy) was wired into the session layer but never propagated to
the surfaces around it, while Gemini CLI stayed documented as a consumer
product despite being enterprise-only since Google's cutover. Gemini keeps
full support; Antigravity now sits beside it everywhere.

Functional fixes:
- docker/agent.Dockerfile never installed agy, so a docker case with
  mode 'antigravity' died on command-not-found. agy is not on npm, so it
  gets its own installer step. --dir /usr/local/bin is load-bearing: the
  default $HOME/.local/bin resolves to root's home at build time and is
  unreachable by the `agent` user the container runs as. Verified inside
  codeman/agent:base (v1.1.10, reachable as `agent`). Note the binary is
  ~190MB, the largest layer in the image.
- Welcome screen gained a Run Antigravity action, gated on agy being
  present like the other CLI buttons, with a cyan identity matching the
  toolbar run button and run-mode dot.
- install.sh now detects agy (search paths mirroring the resolver), counts
  it as a satisfying AI CLI, and recommends it over Gemini in the install
  hints. Detection only, no new auto-install path.

Docs corrected where they were factually wrong:
- architecture-invariants documented isExternalCliMode() as
  opencode/codex/gemini when the code has included antigravity for a
  while, said "all three modes", and omitted ANTIGRAVITY_ from the env
  prefix allowlist row.
- cron-guide's agentType enum, cron-discovery's SessionMode, and
  remote-sessions' RemoteCommandMode were all stale.

Also: README + README.zh-CN (five CLIs, Gemini marked enterprise-only),
package.json keyword, and comment drift in 8 places.

test/run-mode-ui.test.ts now covers the new welcome button; verified it
fails without the settings-ui wiring.

Antigravity nests its whole state under ~/.gemini/antigravity-cli/, not
~/.antigravity, so the existing .gemini docker credential seed already
covers it. Recorded as a comment so nobody adds dead config later.

isAltScreenStripMode() deliberately still excludes antigravity: whether
its TUI needs the alt-screen strip is a behavioural question that needs a
real agy session, not a guess.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

src/web/routes/session-routes.ts

@@ -415,7 +415,7 @@ export function registerSessionRoutes(
     //
     // For keys the caller is actively setting, strip any stale disk entry a prior
     // Codeman version may have written. Scope limited to:
-    //   - Claude mode (OpenCode/Codex/Gemini don't read .claude/settings.local.json)
+    //   - Claude mode (OpenCode/Codex/Gemini/Antigravity don't read .claude/settings.local.json)
     //   - workingDir inside CASES_DIR / the per-user case space (Codeman's managed
     //     territory — we never mutate .claude/settings.local.json in arbitrary user
     //     repos that POST /api/sessions can target, as those may have hand-authored
@@ -2027,7 +2027,7 @@ export function registerSessionRoutes(
       if (!host) return createErrorResponse(ApiErrorCode.NOT_FOUND, 'Remote host not found');
 
       // Per-session config that is applied to the LOCAL tmux/CLI wrapper (env vars via
-      // tmux setenv, effort/model CLI args, codex/gemini/opencode config) does NOT
+      // tmux setenv, effort/model CLI args, codex/gemini/antigravity/opencode config) does NOT
       // cross ssh, so it would silently no-op. Reject rather than pretend it worked —
       // remote command/env customization goes through the per-host command override.
       if (
@@ -2364,7 +2364,7 @@ export function registerSessionRoutes(
         });
         ctx.broadcast(SseEvent.SessionInteractive, { id: session.id, mode: 'shell' });
       } else {
-        // 'claude', 'opencode', 'codex', and 'gemini' modes use startInteractive()
+        // 'claude', 'opencode', 'codex', 'gemini', and 'antigravity' modes use startInteractive()
         await session.startInteractive();
         getLifecycleLog().log({
           event: 'started',