docs: speak the new subscription provider names on every user surface

[code-yeongyu]

Makes every user-facing surface speak the new provider names. Part of #1989 (todo 12).

Renamed (14 places)

Provider guide headings + table, the /fast help text and its RPC error message, the service-tier note in settings.md, the RPC JSON examples' "provider" values, and the provider list in the pi-ai README.

Deliberately NOT renamed — each verified line by line

This is the part that matters, because a blind sweep corrupts real content:

Kept	Why
docs/skills.md:47 "skills from Claude Code or OpenAI Codex"	names OpenAI's actual Codex CLI product, whose skill directories a user adds to settings — not senpi's old display name. Renaming it makes the sentence false.
openai-codex-responses + "OpenAI Codex Responses API"	the frozen wire api id and its dialect name
"OpenAI" / "OpenAI-compatible" / supportsOpenAIGrammarTools	the company/API, not the provider
the outbound originator identity	wire identity sent to the codex backend
claude-sdk-oauth extension dir + release-guide test paths	module paths — owned by the behaviour-free internal rename (todo 10)

OpenAI Codex is simultaneously senpi's old display name (must go) and a real external product senpi interoperates with (must stay). The disambiguation is what the sentence is about, not the token.

Doc drift fixed while sweeping

rpc.md documented the fast-mode error as Fast mode is only available for OpenAI Codex models. — but the shipped string in service-tier.ts:145 already reads "ChatGPT Subscription models." The doc was quoting a message that no longer exists. Now synced to what actually ships.

Verification

Changelog gate PASS (docs-only, no runtime source change). Every remaining legacy mention in docs/ + READMEs is classified above and intentional.

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Summary by cubic

Renames the subscription provider display names and ids on every user-facing surface — provider guide headings, /fast help and its RPC error, the service-tier note in settings.md, RPC JSON examples' "provider" values, and the pi-ai README — as part of #1989. Also renames the "Claude SDK OAuth" heading to "Anthropic Subscription". Docs-only change; no runtime behavior.

Deliberately not renamed

• "OpenAI Codex" stays where it names OpenAI's actual Codex CLI product, whose skill directories users configure — not the provider's old display name.
• "OpenAI"/"OpenAI-compatible", the frozen openai-codex-responses wire API id, and the outbound originator identity refer to the company/API, not the provider.
• Module and test paths (claude-sdk-oauth extension dir, release-guide entries) belong to the behavior-free internal rename.

Doc drift fixed

• rpc.md quoted a fast-mode error that no longer ships; it's now synced to the actual "ChatGPT Subscription models." string.

^{Written for commit c1f105b. Summary will update on new commits.}