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/public/styles.css

@@ -3305,6 +3305,23 @@ body.touch-device .terminal-container .xterm .xterm-helper-textarea {
   transform: translateY(-1px);
 }
 
+/* Antigravity: cyan identity, matching .btn-toolbar.btn-run.mode-antigravity and
+   .run-mode-dot.antigravity so the welcome action reads as the same backend. */
+.welcome-btn-antigravity {
+  background: linear-gradient(135deg, #0b2b33 0%, #0e7490 55%, #0891b2 100%);
+  border-color: rgba(34, 211, 238, 0.4);
+  color: #cffafe;
+  box-shadow: 0 2px 8px rgba(34, 211, 238, 0.16), inset 0 1px 0 rgba(255, 255, 255, 0.06);
+}
+
+.welcome-btn-antigravity:hover {
+  background: linear-gradient(135deg, #124450 0%, #0891b2 55%, #06b6d4 100%);
+  box-shadow: 0 4px 20px rgba(34, 211, 238, 0.3), 0 0 40px rgba(8, 145, 178, 0.12), inset 0 1px 0 rgba(255, 255, 255, 0.08);
+  border-color: rgba(103, 232, 249, 0.5);
+  color: #ecfeff;
+  transform: translateY(-1px);
+}
+
 .welcome-btn-gemini {
   background: linear-gradient(135deg, #10243f 0%, #174ea6 55%, #4f46e5 100%);
   border-color: rgba(96, 165, 250, 0.4);