Update claude-api skill: auth, cloud providers, Managed Agents fixes, token counting (#1276)

* Sync claude-api skill with latest upstream updates

- Add token-counting.md and SKILL.md trigger description update
- Add auth guidance: env credential resolution, ant auth login, OAuth/WIF doc links, 401 causes
- Add mid-conversation system messages (beta) to prompt-caching, agent-design, SKILL.md, Python/TS READMEs
- Add cache pre-warming (max_tokens: 0) section to prompt-caching
- Add Managed Agents pre-flight viability check to onboarding and overview
- Add Bedrock model-ID section to model-migration; add Bedrock row to live-sources
- Add /claude-api migrate subcommand row and migrate-entry callout
- Fix MA networking config: limited type with allow_package_managers/allow_mcp_servers
- Bump MA create-operations rate limit to 300 RPM
- Fix MA SDK drift: sessions.events.stream(), event.name, typed event arrays
- Add SDK coverage: stop_details, error .type, C# tool runner + MA support, Go model constants, Java 2.34.0, client config, response helpers, auto-pagination, advisor tool
- Move Sonnet 4 / Opus 4 to deprecated in models.md

* Add Anthropic CLI and Claude Platform on AWS docs to claude-api skill

- Add shared/anthropic-cli.md: install, auth profiles, OAuth scopes, command
  structure, version-controlled Managed Agents resources, credential traps
- Add shared/claude-platform-on-aws.md: AnthropicAWS clients, SigV4 auth,
  workspace_id, regions, feature availability
- Restore cross-references to both files throughout SKILL.md and the
  managed-agents docs (previously rewritten to live-sources.md pointers)
- Restore Claude Platform on AWS provider taxonomy in SKILL.md, the
  migration-guide section, and live-sources rows

skills/claude-api/shared/token-counting.md

@@ -0,0 +1,56 @@
+# Token Counting
+
+Use the `count_tokens` endpoint (`POST /v1/messages/count_tokens`) for accurate
+token counts against Claude models. Token counts are **model-specific** — pass
+the same model ID you'll use for inference.
+
+**Do not use `tiktoken`.** It's OpenAI's tokenizer. It undercounts Claude
+tokens by ~15–20% on typical text, and by much more on code or non-English
+input. Any estimate from `tiktoken`, `gpt-tokenizer`, or similar is wrong for
+Claude.
+
+## Count a file or string
+
+```python
+from anthropic import Anthropic
+
+client = Anthropic()
+resp = client.messages.count_tokens(
+    model="claude-opus-4-8",
+    messages=[{"role": "user", "content": open("CLAUDE.md").read()}],
+)
+print(resp.input_tokens)
+```
+
+TypeScript: `await client.messages.countTokens({model, messages})` →
+`.input_tokens`. See `{lang}/claude-api/README.md` for other SDKs.
+
+## CLI
+
+```sh
+ant messages count-tokens --model claude-opus-4-8 \
+  --message '{role: user, content: "@./CLAUDE.md"}' \
+  --transform input_tokens -r
+```
+
+## Diffing a file across two versions
+
+The endpoint is stateless — count each version separately and subtract:
+
+```python
+from anthropic import Anthropic
+import subprocess
+
+client = Anthropic()
+def count(text: str) -> int:
+    return client.messages.count_tokens(
+        model="claude-opus-4-8",
+        messages=[{"role": "user", "content": text}],
+    ).input_tokens
+
+before = subprocess.check_output(["git", "show", "HEAD:CLAUDE.md"], text=True)
+after = open("CLAUDE.md").read()
+print(count(after) - count(before))
+```
+
+Full docs: see the Token Counting entry in `shared/live-sources.md`.