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>

docs/remote-sessions.md

@@ -1,7 +1,7 @@
 # Remote Sessions (SSH)
 
 Codeman can run a session's agent on a **remote host over SSH** instead of the
-local machine. The agent (Claude, OpenCode, Codex, Gemini, or a plain shell)
+local machine. The agent (Claude, OpenCode, Codex, Antigravity, Gemini, or a plain shell)
 runs inside a `tmux` server **on the remote host**, so it survives the SSH
 connection dropping; Codeman attaches to it the same way it attaches to a local
 managed session.
@@ -30,7 +30,7 @@ Types live in `src/types/session.ts`; persistence in `src/remote-hosts.ts`.
 | `RemoteHost` (extends `RemoteSshOptions`) | A saved host: `id`, `label`, `host`, `username`, `port?`, `commands?` (per-mode launch command override). |
 | `RemoteCase` | A working directory on a host: `name`, `type: 'remote'`, `hostId`, `remotePath`. |
 | `SessionRemote` (extends `RemoteSshOptions`) | The resolved bundle stamped onto a live session: host coordinates + `remotePath` + `commands`, plus **`owned?`** and **`remoteSessionName?`** (COD-105 — see [Ownership](#ownership-launched-vs-discovered-and-attached-cod-105)). Built by `toSessionRemote(host, case)` (sets `owned: true`) for the launch path, or `toAttachedSessionRemote(host, name, path)` (sets `owned: false`) for the attach path. Both copy the advanced SSH options through so every connection is identical. |
-| `RemoteCommandMode` | `Extract<SessionMode, 'shell' \| 'claude' \| 'opencode' \| 'codex' \| 'gemini'>` — the modes that can run remotely. |
+| `RemoteCommandMode` | `Extract<SessionMode, 'shell' \| 'claude' \| 'opencode' \| 'codex' \| 'gemini' \| 'antigravity'>` — the modes that can run remotely. |
 | `RemoteSessionInfo` (COD-105) | One discovered remote tmux session: `name` (always `codeman-*`), `attached` (a client is connected), `created` (epoch s), `windows`. Returned by `listRemoteCodemanSessions()`. |
 
 Persistence is two flat JSON arrays in the instance data dir:
@@ -115,7 +115,7 @@ Key points:
 - **`exec <cli>`** replaces the pane shell with the agent, so the pane PID *is*
   the agent. The per-mode command comes from `remote.commands?.[mode]` or
   `defaultRemoteCommandForMode(mode)` (`exec claude` / `exec opencode` /
-  `exec codex` / `exec gemini` / `exec bash -l`).
+  `exec codex` / `exec gemini` / `exec agy` / `exec bash -l`).
 - The **whole tmux invocation is a single shell-quoted ssh argument**, and the
   pane command is independently quoted, so a `remotePath` with spaces is safe.
 - Connection options come from the **same `buildSshConnectionArgs(remote)`** as