docs: rename pulumi cloud api to pulumi api

[fallimic]

Summary

• Renames the CLI command from pulumi cloud api to top-level pulumi api across custom docs (breaking change — no backwards-compat fallbacks).
• Renames the --format flag to --output to match the upstream standardization. See pulumi/pulumi#23072.
• Moves the CLI guide content/docs/iac/cli/cloud-api.md → api.md with an alias for SEO on the old URL.
• Updates the LLM agent index (layouts/index.llms.txt) and cross-references in content/docs/reference/cloud-rest-api/, content/docs/iac/automation-api/_index.md, content/docs/administration/access-identity/access-tokens.md, and content/docs/iac/cli/_index.md.
• Leaves auto-generated CLI command docs in content/docs/iac/cli/commands/ untouched. They'll be replaced by the next regen run.
• Preserves "Pulumi Cloud API" (Title Case product/REST API name) in pulumi_login.md, mcp-server/index.md, dynamic-providers.md, deployments.md, _content.gotmpl, and historical blog posts.

Do not merge until

• The new auto-generated CLI command docs (pulumi_api.md, pulumi_api_list.md, pulumi_api_describe.md) land in this repo. Until then, custom doc links to /docs/iac/cli/commands/pulumi_api/, pulumi_api_list/, and pulumi_api_describe/ will 404.
• The upstream CLI ships both renames (pulumi cloud api → pulumi api, --format → --output).

Test plan

• make build succeeds locally
• make lint passes
• After autogen lands: /docs/iac/cli/api/ renders and all links in it resolve
• Old URL /docs/iac/cli/cloud-api/ redirects to /docs/iac/cli/api/ (SEO alias)
• /llms.txt reflects the new command name and --output flag

🤖 Generated with Claude Code

[claude]

Docs review for #18887

Reviewed the rename of pulumi cloud api → pulumi api across docs, cross-references, and llms.txt. The mechanical work is clean and consistent.

What looks good

• New file content/docs/iac/cli/api.md includes the alias /docs/iac/cli/cloud-api/ (line 12) — SEO redirect preserved.
• Menu identifier updated from iac-cli-cloud-api → iac-cli-api (line 9); no other refs to the old identifier remain.
• All call-site files (access-tokens.md, automation-api/_index.md, cli/_index.md, cloud-rest-api/_index.md, cloud-rest-api/api-basics/_index.md) and layouts/index.llms.txt were updated consistently.
• Title-case "Pulumi Cloud API" (product/REST-API name) is correctly preserved where it refers to the API itself rather than the CLI command (mcp-server/index.md, dynamic-providers.md, deployments.md, cloud-rest-api/_content.gotmpl).
• Auto-generated CLI command docs under `content/docs/iac/cli/commands/pulumi_cloud_api*.md` were intentionally left untouched — correct, since the next regen run will replace them. The "Do not merge until" callout flags this risk well.

Issues / suggestions

1. Page `title` no longer matches the URL/command — `content/docs/iac/cli/api.md` line 2

The frontmatter still reads `title: Calling the Cloud API`, but the URL is now `/docs/iac/cli/api/`, the command is `pulumi api`, the `h1` is "Calling the Pulumi Cloud REST API from the CLI", and the `title_tag` is "Pulumi CLI: Calling the Pulumi Cloud REST API". The nav title is the odd one out — "Calling the Cloud API" is ambiguous (Automation API? Cloud REST API?) and inconsistent with how the page now reads. Recommend aligning it with the h1/title_tag for clarity.

```suggestion
title: Calling the Pulumi Cloud REST API
```

2. OpenAPI cache directory path may be stale — `content/docs/iac/cli/api.md` line 79

The doc says the CLI caches the spec under `$PULUMI_HOME/cloud-api-cache//spec.json`. If the upstream CLI rename also changed the cache directory name (e.g., to `api-cache/`), this line is wrong. Worth verifying against the CLI source — if the cache path was kept as `cloud-api-cache` for back-compat, leave as-is; otherwise update.

3. Minor — sentence-case heading check passes

H2s in `api.md` (Subcommands, Authentication, Path-template substitution, Request flags, OpenAPI spec caching, Exit codes and error envelope, Examples, See also) are sentence case per AGENTS.md.

Out of scope but worth noting

The pre-existing links to `/docs/pulumi-cloud/cloud-rest-api/` in `dynamic-providers.md` and `mcp-server/index.md` (different from `/docs/reference/cloud-rest-api/`) are not introduced by this PR and resolve via existing aliases — but they're worth normalizing in a follow-up.

---

The "do not merge until autogen lands" gate is correctly identified — the three command-reference links (`/docs/iac/cli/commands/pulumi_api/`, `pulumi_api_list/`, `pulumi_api_describe/`) will 404 until then. No additional blockers from the docs side.

Mention me (@claude) if you'd like another pass after addressing these, or want me to look at anything specific in more detail.

[pulumi-bot]

Your site preview for commit 59bbb30 is ready! 🎉

http://www-testing-pulumi-docs-origin-pr-18887-59bbb30b.s3-website.us-west-2.amazonaws.com

[pulumi-bot]

Lighthouse Performance Report

Commit: 59bbb30 | Metric definitions

Page	Device	Score	FCP	LCP	TBT	CLS	SI
Homepage	Mobile	🟡 64	2.9s	2.9s	862ms	0.019	6.6s
Homepage	Desktop	🟢 96	0.8s	1.3s	24ms	0.005	1.2s
Install Pulumi	Mobile	🔴 37	5.2s	7.6s	262ms	0.454	5.2s
Install Pulumi	Desktop	🟢 90	1.2s	1.7s	20ms	0.026	1.4s
AWS Get Started	Mobile	🟡 54	5.0s	7.6s	236ms	0.086	7.3s
AWS Get Started	Desktop	🟡 86	1.1s	1.6s	21ms	0.033	2.8s