core/agent: run a hosted search as the surface's own tool

DeepSeek's Anthropic compat runs a hosted ``web_search`` itself and answers with
the blocks that search produced — ``thinking``, ``server_tool_use`` (the query)
and ``web_search_tool_result`` — so the content union that knew only text and
tool_use could not decode a live search turn. It carries them now, ``tools``
accepts the opaque server-tool dicts the surface declares, and
``web_search_tool_result.content`` stays loose on purpose: its
``web_search_result`` entries hold an ``encrypted_content`` the API demands back
unchanged (a trimmed result is answered with 422 "missing field
``encrypted_content``").

``provider_tools`` reached only the Responses surface, and the Anthropic one
wants its own definition of the same intent: a bare ``web_search`` becomes
``{type="web_search_20250305", name="web_search"}`` (the server tool Claude
declares and DeepSeek's compat reads, keeping a ``max_uses`` cap or any other
key), merged after the local function tools.

Such a tool is the server's: it streams ``input_json_delta`` fragments like a
call, and reading them as one asked the registry for a tool the server had
already run. Block types are now tracked, so only a ``tool_use`` block becomes a
tool call; the search blocks and ``thinking`` are skipped by the response
mapping (the answer the model wrote already used them) and never executed.

tests/test_lmproto/test_anthropic.py

@@ -13,6 +13,7 @@ from plyngent.lmproto.anthropic.model import (
     AnthropicResponseText,
     AnthropicUsage,
     AnthropicUserMessage,
+    AnthropicWebSearchToolResultContent,
 )
 
 
@@ -44,6 +45,75 @@ def test_messages_param_encode_omits_defaults() -> None:
 
 
 @pytest.mark.asyncio
+async def test_client_decodes_a_server_side_search_response(monkeypatch: pytest.MonkeyPatch) -> None:
+    """DeepSeek's Anthropic compat answers a search turn with server tool blocks.
+
+    A live turn reads ``thinking, server_tool_use, web_search_tool_result, text``
+    (the results carry an ``encrypted_content`` the API demands back unchanged);
+    the response must decode, even though none of those blocks is a local call.
+    """
+    body = {
+        "id": "msg_search",
+        "type": "message",
+        "role": "assistant",
+        "model": "deepseek-flash",
+        "stop_reason": "end_turn",
+        "content": [
+            {"type": "thinking", "thinking": "Let me search.", "signature": "b032a4ad-87fe-42ce-801d-e33dd743d8b9"},
+            {
+                "type": "server_tool_use",
+                "id": "call_00_joE6PEEC1otU8pvSe4zY3017",
+                "name": "web_search",
+                "input": {"query": "DeepSeek latest news"},
+                "caller": {"type": "direct"},
+            },
+            {
+                "type": "web_search_tool_result",
+                "tool_use_id": "call_00_joE6PEEC1otU8pvSe4zY3017",
+                "content": [
+                    {
+                        "type": "web_search_result",
+                        "title": "Change Log | DeepSeek API Docs",
+                        "url": "https://api-docs.deepseek.com/updates/",
+                        "encrypted_content": "sd918tZXSvVp6j7ermvF4cl/lspbqHzths9SMQw6ziEw",
+                    }
+                ],
+            },
+            {"type": "text", "text": "DeepSeek shipped a new model."},
+        ],
+        "usage": {"input_tokens": 16592, "output_tokens": 1419, "server_tool_use": {"web_search_requests": 4}},
+    }
+    client = AnthropicClient(AnthropicConfig(api_key="sk-test", base_url="https://example/v1"))
+
+    class _Resp:
+        status_code = 200
+        content = msgspec.json.encode(body)
+
+    async def fake_post(path: str, **kwargs: object) -> _Resp:
+        return _Resp()
+
+    monkeypatch.setattr(client.session, "post", fake_post)
+    result = await client.messages(AnthropicMessagesParam(model="deepseek-flash", messages=[]))
+    kinds = [block.__struct_config__.tag for block in result.content]
+    assert kinds == ["thinking", "server_tool_use", "web_search_tool_result", "text"]
+    search = result.content[2]
+    assert isinstance(search, AnthropicWebSearchToolResultContent)
+    assert search.tool_use_id == "call_00_joE6PEEC1otU8pvSe4zY3017"
+    assert search.content[0]["encrypted_content"].startswith("sd918tZXSvVp")
+    assert result.content[3].text == "DeepSeek shipped a new model."
+
+
+def test_messages_param_encodes_server_tool_dicts() -> None:
+    """A hosted tool goes on the wire as the server-tool dict the surface wants."""
+    param = AnthropicMessagesParam(
+        model="deepseek-flash",
+        messages=[AnthropicUserMessage(content="hi")],
+        tools=[{"type": "web_search_20250305", "name": "web_search", "max_uses": 3}],
+    )
+    data = msgspec.json.decode(msgspec.json.encode(param))
+    assert data["tools"] == [{"type": "web_search_20250305", "name": "web_search", "max_uses": 3}]
+
+
 async def test_client_messages_create(monkeypatch: pytest.MonkeyPatch) -> None:
     client = AnthropicClient(AnthropicConfig(api_key="sk-test", base_url="https://example/v1"))