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>

docker/agent.Dockerfile

@@ -26,8 +26,8 @@ RUN apt-get update \
       openssh-client \
  && rm -rf /var/lib/apt/lists/*
 
-# The agent CLIs (all four backends Codeman supports). Pinning is left to the
-# rebuild cadence (see docs/docker-cases-plan.md, user-decision 2).
+# The npm-published agent CLIs. Pinning is left to the rebuild cadence (see
+# docs/docker-cases-plan.md, user-decision 2).
 RUN npm install -g \
       @anthropic-ai/claude-code \
       @openai/codex \
@@ -35,6 +35,15 @@ RUN npm install -g \
       opencode-ai \
  && npm cache clean --force
 
+# Antigravity (`agy`) is NOT on npm — Google ships a standalone binary through its
+# own installer, so it needs its own step. `--dir /usr/local/bin` is load-bearing:
+# the installer's default target is `$HOME/.local/bin`, which at build time is
+# root's home and would be unreachable by the `agent` user the container runs as.
+# ⚠️ This binary is ~190MB on its own; it is the single largest layer in the image.
+RUN curl -fsSL https://antigravity.google/cli/install.sh | bash -s -- --dir /usr/local/bin \
+ && chmod 755 /usr/local/bin/agy \
+ && agy --version
+
 # `agent` user (gid 0) with an arbitrary-uid-writable HOME. The uid is
 # auto-assigned (node:22-slim already occupies uid 1000 with its `node` user); at
 # runtime Codeman overrides with `--user <hostUid>:0` on Linux, so the baked uid
@@ -50,7 +59,8 @@ ENV HOME=/home/agent
 # dirs: tokens/settings/config are seeded in as writable copies and each CLI's runtime
 # state (backups, tasks, refreshed tokens) stays container-local, while ONLY the shared
 # transcript/rollout dirs (`.claude/projects`, `.codex/sessions`) are bind-mounted from
-# the host. (gemini/gcloud/opencode are whole seed-copies and need no pre-created dir.)
+# the host. (gemini/gcloud/opencode are whole seed-copies and need no pre-created dir;
+# Antigravity nests its state inside `.gemini/antigravity-cli`, so it rides that seed.)
 RUN useradd -g 0 -m -d /home/agent -s /bin/bash agent \
  && mkdir -p /home/agent/.npm /home/agent/.cache /home/agent/.config /home/agent/.codeman \
       /home/agent/.claude/projects /home/agent/.codex/sessions \