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>

packages/xterm-zerolag-input/README.md

@@ -16,7 +16,7 @@
 
 > ### Made for [**Codeman**](https://getcodeman.com)
 >
-> This overlay is the local echo engine of [**Codeman**](https://github.com/Ark0N/Codeman), mission control for AI coding agents: run and monitor a dozen Claude Code, Codex, OpenCode and Gemini sessions at once, watch their subagents work in live floating windows, let them run autonomously overnight, and drive all of it from your phone.
+> This overlay is the local echo engine of [**Codeman**](https://github.com/Ark0N/Codeman), mission control for AI coding agents: run and monitor a dozen Claude Code, Codex, OpenCode and Antigravity sessions at once, watch their subagents work in live floating windows, let them run autonomously overnight, and drive all of it from your phone.
 >
 > That last part is why this library exists. The demo below is a real Codeman session on two phones.