refactor(cli): route /model picker through shared inventory module

The interactive CLI /model picker was the third call-site duplicating
the inline config-slice + list_authenticated_providers pattern that
PR #23666 consolidated for the dashboard and TUI. Route it through
load_picker_context() + build_models_payload() too so all surfaces
that show authenticated providers share one substrate.

Side effect: cli.py now also benefits from the latent v12+ keyed
providers fix (custom_providers populated via
get_compatible_custom_providers, not cfg.get raw).

The aux-task switcher (hermes_cli/main.py) and gateway model
switcher (gateway/run.py) deliberately stay on the legacy path —
they use different config sections (auxiliary.<task>.*) and a
different config loader (_load_gateway_config) respectively, so
forcing them through ConfigContext would either overload its
semantics or grow the module past the clean refactor scope.

cli.py

@@ -6614,7 +6614,7 @@ class HermesCLI:
           /model <name> --provider <provider> — switch provider + model
           /model --provider <provider>        — switch to provider, auto-detect model
         """
-        from hermes_cli.model_switch import switch_model, parse_model_flags, list_authenticated_providers
+        from hermes_cli.model_switch import switch_model, parse_model_flags
         from hermes_cli.providers import get_label
 
         # Parse args from the original command
@@ -6624,16 +6624,25 @@ class HermesCLI:
         # Parse --provider and --global flags
         model_input, explicit_provider, persist_global = parse_model_flags(raw_args)
 
-        # Load providers for switch_model (picker path needs them below)
-        user_provs = None
-        custom_provs = None
+        # Single inventory context — replaces the inline config-slice the
+        # dashboard / TUI used to duplicate. Overlay live session state
+        # via with_overrides (truthy-only) so empty self.* attrs don't
+        # clobber disk config.
+        from hermes_cli.inventory import build_models_payload, load_picker_context
+
         try:
-            from hermes_cli.config import get_compatible_custom_providers, load_config
-            cfg = load_config()
-            user_provs = cfg.get("providers")
-            custom_provs = get_compatible_custom_providers(cfg)
+            ctx = load_picker_context().with_overrides(
+                current_provider=self.provider or "",
+                current_model=self.model or "",
+                current_base_url=self.base_url or "",
+            )
         except Exception:
-            pass
+            ctx = None
+
+        # switch_model() + _open_model_picker still need the raw provider
+        # dicts; ConfigContext is the canonical source for both.
+        user_provs = ctx.user_providers if ctx is not None else None
+        custom_provs = ctx.custom_providers if ctx is not None else None
 
         # No args at all: open prompt_toolkit-native picker modal
         if not model_input and not explicit_provider:
@@ -6641,14 +6650,9 @@ class HermesCLI:
             provider_display = get_label(self.provider) if self.provider else "unknown"
 
             try:
-                providers = list_authenticated_providers(
-                    current_provider=self.provider or "",
-                    current_base_url=self.base_url or "",
-                    current_model=self.model or "",
-                    user_providers=user_provs,
-                    custom_providers=custom_provs,
-                    max_models=50,
-                )
+                if ctx is None:
+                    raise RuntimeError("inventory context unavailable")
+                providers = build_models_payload(ctx, max_models=50)["providers"]
             except Exception:
                 providers = []