refactor(lead-agent): make build_middlewares public to drop the last cross-module private import (#3458)

`client.py` imported the private `_build_middlewares` from `agent.py` across a
module boundary and called it as public API. Because the `_` name signals
"module-private, no external callers", any future rename or signature change
silently breaks the embedded `DeerFlowClient` path — and the test suite even
monkeypatched `deerflow.client._build_middlewares`, baking the leak in.

`DeerFlowClient` is a lead-agent variant that genuinely needs the lead agent's
full middleware composition, so make the dependency honest: promote the helper
to a documented public entry point `build_middlewares` and update every in-repo
caller. Found during #3341 review; #3341 already removed one such leak
(`_assemble_deferred` -> public `assemble_deferred_tools`) and left this one out
of scope on purpose.

- agent.py: rename def + both internal call sites; expand the docstring into a
  public-entry-point contract and document the previously-undocumented
  model_name / app_config / deferred_setup params
- client.py: import + call site now use the public name (removes the last
  cross-module private import)
- scripts/tool-error-degradation-detection.sh: update its import + call site
- tests (5 files): update monkeypatch/patch targets and direct calls
- docs (backend/CLAUDE.md, plan_mode_usage.md, middlewares.mdx): sync the live
  references that describe the symbol as current API

Pure mechanical rename, no behavior change. Historical design docs (rfc,
superpowers spec) intentionally keep the old name as point-in-time records.

Closes #3431

backend/tests/test_lead_agent_skills.py

@@ -139,7 +139,7 @@ def test_make_lead_agent_empty_skills_passed_correctly(monkeypatch):
     monkeypatch.setattr(lead_agent_module, "create_chat_model", lambda **kwargs: "model")
     monkeypatch.setattr("deerflow.tools.get_available_tools", lambda **kwargs: [])
     monkeypatch.setattr(lead_agent_module, "_load_enabled_skills_for_tool_policy", lambda available_skills, *, app_config: [])
-    monkeypatch.setattr(lead_agent_module, "_build_middlewares", lambda *args, **kwargs: [])
+    monkeypatch.setattr(lead_agent_module, "build_middlewares", lambda *args, **kwargs: [])
     monkeypatch.setattr(lead_agent_module, "create_agent", lambda **kwargs: kwargs)
 
     class MockModelConfig:
@@ -180,7 +180,7 @@ def test_make_lead_agent_filters_tools_from_available_skills(monkeypatch):
 
     monkeypatch.setattr(lead_agent_module, "_resolve_model_name", lambda x=None, **kwargs: "default-model")
     monkeypatch.setattr(lead_agent_module, "create_chat_model", lambda **kwargs: "model")
-    monkeypatch.setattr(lead_agent_module, "_build_middlewares", lambda *args, **kwargs: [])
+    monkeypatch.setattr(lead_agent_module, "build_middlewares", lambda *args, **kwargs: [])
     monkeypatch.setattr(lead_agent_module, "apply_prompt_template", lambda **kwargs: "mock_prompt")
     monkeypatch.setattr(lead_agent_module, "create_agent", lambda **kwargs: kwargs)
     monkeypatch.setattr(lead_agent_module, "load_agent_config", lambda x: AgentConfig(name="test", skills=["restricted", "legacy"]))
@@ -203,7 +203,7 @@ def test_make_lead_agent_all_legacy_skills_preserve_all_tools(monkeypatch):
 
     monkeypatch.setattr(lead_agent_module, "_resolve_model_name", lambda x=None, **kwargs: "default-model")
     monkeypatch.setattr(lead_agent_module, "create_chat_model", lambda **kwargs: "model")
-    monkeypatch.setattr(lead_agent_module, "_build_middlewares", lambda *args, **kwargs: [])
+    monkeypatch.setattr(lead_agent_module, "build_middlewares", lambda *args, **kwargs: [])
     monkeypatch.setattr(lead_agent_module, "apply_prompt_template", lambda **kwargs: "mock_prompt")
     monkeypatch.setattr(lead_agent_module, "create_agent", lambda **kwargs: kwargs)
     monkeypatch.setattr(lead_agent_module, "load_agent_config", lambda x: AgentConfig(name="test", skills=None))
@@ -227,7 +227,7 @@ def test_make_lead_agent_enforces_allowed_tools_when_skill_cache_is_cold(monkeyp
 
     monkeypatch.setattr(lead_agent_module, "_resolve_model_name", lambda x=None, **kwargs: "default-model")
     monkeypatch.setattr(lead_agent_module, "create_chat_model", lambda **kwargs: "model")
-    monkeypatch.setattr(lead_agent_module, "_build_middlewares", lambda *args, **kwargs: [])
+    monkeypatch.setattr(lead_agent_module, "build_middlewares", lambda *args, **kwargs: [])
     monkeypatch.setattr(lead_agent_module, "apply_prompt_template", lambda **kwargs: "mock_prompt")
     monkeypatch.setattr(lead_agent_module, "create_agent", lambda **kwargs: kwargs)
     monkeypatch.setattr(lead_agent_module, "load_agent_config", lambda x: AgentConfig(name="test", skills=["restricted"]))