docs: Added documentation on the new OpenAI OAuth support

Clients.md

@@ -128,10 +128,33 @@ coyote --authenticate
 Alternatively, you can use the REPL command `.authenticate`.
 
 This opens your browser for the OAuth authorization flow. Depending on the provider, Coyote will either start a
-temporary localhost server to capture the callback automatically (e.g. Gemini) or ask you to paste the authorization
+temporary localhost server to capture the callback automatically (e.g. Gemini, OpenAI) or ask you to paste the authorization
-code back into the terminal (e.g. Claude). Coyote stores the tokens in `~/.cache/coyote/oauth` and automatically refreshes
+code back into the terminal (e.g. Claude). Coyote stores the tokens in `<coyote_cache_dir>/coyote/oauth` and automatically refreshes
 them when they expire.
 
+### OpenAI OAuth Note
+
+OpenAI OAuth requires a **ChatGPT Plus or Pro subscription**. It uses the shared Codex CLI OAuth app registered with
+OpenAI, so no additional API credentials or app registration are needed.
+
+When authenticating, Coyote starts a localhost server on port **1455** to capture the OAuth callback automatically. This port is
+fixed by OpenAI's app registration and cannot be changed. Make sure port 1455 is available when you run
+`--authenticate`/`.authenticate`.
+
+When `auth: oauth` is set and no `api_base` is configured, Coyote automatically routes all requests through
+`chatgpt.com/backend-api/codex/responses` (the OpenAI Responses API), which is what ChatGPT Plus/Pro subscribers have
+access to. If you later add an `api_key` or a custom `api_base`, Coyote will use the standard `api.openai.com/v1`
+endpoint instead.
+
+Example configuration:
+
+```yaml
+clients:
+  - type: openai
+    name: openai-oauth
+    auth: oauth
+```
+
 ### Gemini OAuth Note
 Coyote uses the following scopes for OAuth with Gemini:
 * https://www.googleapis.com/auth/generative-language.peruserquota 
@@ -165,6 +188,7 @@ coyote -m my-claude-oauth:claude-sonnet-4-20250514 "Hello!"
 ## Providers That Support OAuth
 * Claude
 * Gemini
+* OpenAI (requires ChatGPT Plus or Pro subscription)
 
 # Extra Settings
 Coyote also lets you customize some extra settings for interacting with APIs: