fix(auxiliary): widen URL rewrite + main_runtime to sibling custom branches

Follow-up to PR #16819 applying the same treatment to the two sibling
fallback sites in resolve_provider_client() that carry the identical bug
class as the anonymous-custom branch:

- Named custom provider (providers: / custom_providers: config entries):
  apply _to_openai_base_url() on the OpenAI-wire path (chat_completions /
  codex_responses), leave custom_base untouched on the anthropic_messages
  path where the /anthropic surface is intentional.  Prefer
  main_runtime.get('model') over _read_main_model() so the entry model
  still wins first.  The ImportError fallback for anthropic_messages now
  redoes query-param extraction against the rewritten URL so the final
  OpenAI client hits /v1.

- external_process branch (copilot-acp): same main_runtime.get('model')
  fallback before _read_main_model() so auxiliary tasks on this provider
  track live /model switches instead of stale config.yaml.

Keeps the fix consistent across all three custom-endpoint fallback sites
in resolve_provider_client().

agent/auxiliary_client.py

@@ -1895,10 +1895,22 @@ def resolve_provider_client(
             entry_api_mode = (api_mode or custom_entry.get("api_mode") or "").strip()
             if custom_base:
                 final_model = _normalize_resolved_model(
-                    model or custom_entry.get("model") or _read_main_model() or "gpt-4o-mini",
+                    model
+                    or custom_entry.get("model")
+                    or (main_runtime.get("model") if main_runtime else None)
+                    or _read_main_model()
+                    or "gpt-4o-mini",
                     provider,
                 )
-                _clean_base2, _dq2 = _extract_url_query_params(custom_base)
+                # anthropic_messages talks to the /anthropic surface directly;
+                # OpenAI-wire paths (chat_completions / codex_responses) need the
+                # /v1 equivalent.  Rewrite only on the OpenAI-wire path so the
+                # Anthropic fallback SDK still sees the original URL.
+                if entry_api_mode == "anthropic_messages":
+                    openai_base = custom_base
+                else:
+                    openai_base = _to_openai_base_url(custom_base)
+                _clean_base2, _dq2 = _extract_url_query_params(openai_base)
                 _extra2 = {"default_query": _dq2} if _dq2 else {}
                 logger.debug(
                     "resolve_provider_client: named custom provider %r (%s, api_mode=%s)",
@@ -1917,7 +1929,12 @@ def resolve_provider_client(
                             "installed — falling back to OpenAI-wire.",
                             provider,
                         )
-                        client = OpenAI(api_key=custom_key, base_url=_clean_base2, **_extra2)
+                        # Fallback went OpenAI-wire after all — redo the query
+                        # extraction against the rewritten /v1 URL.
+                        _fallback_base = _to_openai_base_url(custom_base)
+                        _fb_clean, _fb_dq = _extract_url_query_params(_fallback_base)
+                        _fb_extra = {"default_query": _fb_dq} if _fb_dq else {}
+                        client = OpenAI(api_key=custom_key, base_url=_fb_clean, **_fb_extra)
                         return (_to_async_client(client, final_model, is_vision=is_vision) if async_mode
                                 else (client, final_model))
                     sync_anthropic = AnthropicAuxiliaryClient(
@@ -1936,7 +1953,7 @@ def resolve_provider_client(
                 ):
                     client = CodexAuxiliaryClient(client, final_model)
                 else:
-                    client = _wrap_if_needed(client, final_model, custom_base)
+                    client = _wrap_if_needed(client, final_model, openai_base)
                 return (_to_async_client(client, final_model, is_vision=is_vision) if async_mode
                         else (client, final_model))
             logger.warning(
@@ -2038,7 +2055,12 @@ def resolve_provider_client(
 
     if pconfig.auth_type == "external_process":
         creds = resolve_external_process_provider_credentials(provider)
-        final_model = _normalize_resolved_model(model or _read_main_model(), provider)
+        final_model = _normalize_resolved_model(
+            model
+            or (main_runtime.get("model") if main_runtime else None)
+            or _read_main_model(),
+            provider,
+        )
         if provider == "copilot-acp":
             api_key = str(creds.get("api_key", "")).strip()
             base_url = str(creds.get("base_url", "")).strip()