feat(settings): configure the OpenAI-compatible gateway from Settings

Its own form with its own three fields, its own entry in the provider
dropdown and in the fallback-chain editor, and copy in six locales that
says plainly where the OpenAI key does not go.

The chain editor offers the entry but the default chain does not carry
it: it resolves only against a base URL somebody saved.

The read endpoint reports the gateway's base URL and model, and the
bearer as presence only. OpenAPI regenerated.

docs/api/openapi.yaml

@@ -4477,10 +4477,10 @@ paths:
       tags:
         - Auth
       summary: Read the calling user's AI-provider configuration
-      description: "Returns the user's selected provider/model/baseUrl plus the effective availability: `aiAvailable` is true
-        when any provider can serve the user (BYOK, self-hosted, or the operator's server-managed key), and `managedBy`
-        reports which. iOS gates Coach visibility off these two fields. Key material is reported as presence + a 4-char
-        masked preview only."
+      description: "Returns the user's selected provider/model/baseUrl (plus the OpenAI-compatible gateway's own base URL and
+        model) and the effective availability: `aiAvailable` is true when any provider can serve the user (BYOK,
+        self-hosted, or the operator's server-managed key), and `managedBy` reports which. iOS gates Coach visibility
+        off these two fields. Key material is reported as presence + a 4-char masked preview only."
       responses:
         "200":
           description: Resolved AI-provider configuration.
@@ -21942,6 +21942,7 @@ components:
                 - OPENAI
                 - ANTHROPIC
                 - LOCAL
+                - OPENAI_COMPATIBLE
                 - CHATGPT_OAUTH
             - type: "null"
           description: The user's selected provider, or null when none is set.
@@ -21984,6 +21985,21 @@ components:
             - type: string
             - type: "null"
           description: "`...` + last 4 chars of the stored OpenAI key, or null."
+        compatBaseUrl:
+          anyOf:
+            - type: string
+            - type: "null"
+          description: "v1.33.1 (#470) — base URL of the OpenAI-compatible gateway (LiteLLM / OpenRouter / vLLM). Its own column:
+            the OpenAI provider stays pinned to api.openai.com and never reads it."
+        compatModel:
+          anyOf:
+            - type: string
+            - type: "null"
+          description: Model the gateway should route. Null falls back to `model`; with neither set the gateway entry does not
+            resolve.
+        hasCompatKey:
+          type: boolean
+          description: Whether a bearer is stored for the gateway. The bearer is optional — a gateway without auth needs none.
         responseTimeoutSeconds:
           anyOf:
             - type: integer
@@ -22003,6 +22019,9 @@ components:
         - hasLocalKey
         - hasOpenaiKey
         - openaiKeyPreview
+        - compatBaseUrl
+        - compatModel
+        - hasCompatKey
         - responseTimeoutSeconds
       additionalProperties: false
       description: The calling user's AI-provider configuration plus the effective availability (`aiAvailable` + `managedBy`).