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_client.py

@@ -910,7 +910,7 @@ class TestEnsureAgent:
         with (
             patch("deerflow.client.create_chat_model"),
             patch("deerflow.client.create_agent", return_value=mock_agent),
-            patch("deerflow.client._build_middlewares", return_value=[]) as mock_build_middlewares,
+            patch("deerflow.client.build_middlewares", return_value=[]) as mock_build_middlewares,
             patch("deerflow.client.apply_prompt_template", return_value="prompt") as mock_apply_prompt,
             patch.object(client, "_get_tools", return_value=[]),
             patch("deerflow.runtime.checkpointer.get_checkpointer", return_value=MagicMock()),
@@ -935,7 +935,7 @@ class TestEnsureAgent:
         with (
             patch("deerflow.client.create_chat_model"),
             patch("deerflow.client.create_agent", return_value=mock_agent) as mock_create_agent,
-            patch("deerflow.client._build_middlewares", return_value=[]),
+            patch("deerflow.client.build_middlewares", return_value=[]),
             patch("deerflow.client.apply_prompt_template", return_value="prompt"),
             patch.object(client, "_get_tools", return_value=[]),
             patch("deerflow.runtime.checkpointer.get_checkpointer", return_value=mock_checkpointer),
@@ -960,7 +960,7 @@ class TestEnsureAgent:
         with (
             patch("deerflow.client.create_chat_model"),
             patch("deerflow.client.create_agent", return_value=mock_agent) as mock_create_agent,
-            patch("deerflow.client._build_middlewares", side_effect=fake_build_middlewares),
+            patch("deerflow.client.build_middlewares", side_effect=fake_build_middlewares),
             patch("deerflow.client.apply_prompt_template", return_value="prompt"),
             patch.object(client, "_get_tools", return_value=[]),
             patch("deerflow.runtime.checkpointer.get_checkpointer", return_value=MagicMock()),
@@ -979,7 +979,7 @@ class TestEnsureAgent:
         with (
             patch("deerflow.client.create_chat_model"),
             patch("deerflow.client.create_agent", return_value=mock_agent) as mock_create_agent,
-            patch("deerflow.client._build_middlewares", return_value=[]),
+            patch("deerflow.client.build_middlewares", return_value=[]),
             patch("deerflow.client.apply_prompt_template", return_value="prompt"),
             patch.object(client, "_get_tools", return_value=[]),
             patch("deerflow.runtime.checkpointer.get_checkpointer", return_value=None),
@@ -1957,7 +1957,7 @@ class TestScenarioAgentRecreation:
         with (
             patch("deerflow.client.create_chat_model"),
             patch("deerflow.client.create_agent", side_effect=fake_create_agent),
-            patch("deerflow.client._build_middlewares", return_value=[]),
+            patch("deerflow.client.build_middlewares", return_value=[]),
             patch("deerflow.client.apply_prompt_template", return_value="prompt"),
             patch.object(client, "_get_tools", return_value=[]),
             patch("deerflow.runtime.checkpointer.get_checkpointer", return_value=MagicMock()),
@@ -1985,7 +1985,7 @@ class TestScenarioAgentRecreation:
         with (
             patch("deerflow.client.create_chat_model"),
             patch("deerflow.client.create_agent", side_effect=fake_create_agent),
-            patch("deerflow.client._build_middlewares", return_value=[]),
+            patch("deerflow.client.build_middlewares", return_value=[]),
             patch("deerflow.client.apply_prompt_template", return_value="prompt"),
             patch.object(client, "_get_tools", return_value=[]),
             patch("deerflow.runtime.checkpointer.get_checkpointer", return_value=MagicMock()),
@@ -2010,7 +2010,7 @@ class TestScenarioAgentRecreation:
         with (
             patch("deerflow.client.create_chat_model"),
             patch("deerflow.client.create_agent", side_effect=fake_create_agent),
-            patch("deerflow.client._build_middlewares", return_value=[]),
+            patch("deerflow.client.build_middlewares", return_value=[]),
             patch("deerflow.client.apply_prompt_template", return_value="prompt"),
             patch.object(client, "_get_tools", return_value=[]),
             patch("deerflow.runtime.checkpointer.get_checkpointer", return_value=MagicMock()),