Docs: cover Antigravity, correct stale references, verify every example

[burakdede]

Documentation-only pass over the README and the doc site. No source changes.

Antigravity was undocumented

It has been a supported tool since #45, but was absent from the README and 11 of 17 doc pages. It is now covered everywhere the other three tools are: support matrix, command reference, contexts, shell hooks, config schema, and workspace guardrails — including its two real constraints:

• OAuth-only. --api-key, --api-key-stdin, and --from-env are rejected for it.
• No documented per-profile auth root, so switching replaces the shared live session and --state-mode does not apply.

Claims that did not match the binary

Each of these was checked against real CLI output rather than read for plausibility:

Documented	Actual
oauth_account.json	oauth-account.json
Backup id 20260325T114502Z-claude-work	2026-03-25T11-45-02.123Z-0000, nested <id>/<tool>/<profile>/
jq 'select(.token_warning != null)'	No such field in status --json
jq 'select(.profile == "claude/work") | sort_by(.created_at)'	Backups have no created_at; profile is "work"
aisw list codex --json | jq '.profiles[].name'	Output is grouped by tool — this iterated null
Quickstart: --from-live listed under "Interactive OAuth"	The opposite — it captures without launching login

The three jq examples were copy-paste-broken for anyone scripting against them.

Reference gaps filled

Missing --json on use / remove / rename / backup restore; missing --tool / --search / --sort / --active-only on list, status, and backup list; missing --antigravity on context create / set / unset; global flags absent from the README entirely.

Previously unwritten behavior

• Exit codes (0 / 1 / 2) and the JSON failure envelope, with a note to branch on the stable error.kind rather than the message text
• ~/.aisw/workspaces.json — the workspace rules file was not documented at all
• use --all skip-vs-fail semantics
• Duplicate-account detection (by key for API keys, by identity for OAuth)
• API-key charset validation
• uninstall --remove-data also purging keyring entries
• New troubleshooting entries for the errors users will actually hit

Site generator

website/scripts/sync-docs.mjs hardcodes the SEO descriptions and hero tagline, and those override the doc frontmatter. Fixing the docs alone would have left the site's meta descriptions stale, so the generator was updated too (including adding Antigravity to the keyword list).

Verification

• Every documented command resolves to a real subcommand (45 distinct paths)
• 35 documented workflows execute end to end against the real binary
• All 16 documented jq pipelines run clean against real output
• Site builds (15 pages); npm run check:seo passes
• Rust suite unaffected: 921 passing, 0 failing

Merge order

#49 is already merged, so every statement here matches main as it stands. No ordering constraint remains.