fix: retry web searches after key-specific failures - #10877

Please address the comments from this code review:

## Individual Comments

### Comment 1
<location path="astrbot/core/tools/web_search_tools.py" line_range="258" />
<code_context>
                 reason = await response.text()
                 # Retryable errors are saved so the final failure is meaningful.
-                if response.status in _RETRYABLE_HTTP_STATUSES:
+                if response.status in _TAVILY_RETRYABLE_HTTP_STATUSES:
                     last_error = Exception(
                         f"Tavily web search failed: {reason}, status: {response.status}",
</code_context>
<issue_to_address>
**Usable search keys go untried**

When concurrent requests advance the same provider's rotator between a failed attempt and its retry, the Tavily, Exa, and DeepSeek retry loops call the shared `_KeyRotator.get` again, so a request can reuse a key it already tried and exhaust its attempts without trying a usable configured key; the caller sees a search or fetch failure.

Track keys tried by each request and select an untried key for each retry instead of reacquiring one from the shared rotator.

Also at `astrbot/core/tools/web_search_tools.py:314`, `astrbot/core/tools/web_search_tools.py:442-453`, `astrbot/core/tools/web_search_tools.py:1069-1070`, `astrbot/core/tools/web_search_tools.py:1125`, `astrbot/core/tools/web_search_tools.py:1636-1637`, `astrbot/core/tools/web_search_tools.py:1654`, `astrbot/core/tools/web_search_tools.py:1698-1699`, `astrbot/core/tools/web_search_tools.py:1716`, `astrbot/core/tools/web_search_tools.py:2172-2173`, `astrbot/core/tools/web_search_tools.py:2190`, `astrbot/core/tools/web_search_tools.py:2278-2279`, `astrbot/core/tools/web_search_tools.py:2296`.
</issue_to_address>

### Comment 2
<location path="tests/unit/test_web_search_tools.py" line_range="1837" />
<code_context>
+        with pytest.raises(Exception, match=f"last key failed, status: {status}"):
+            await search_function(settings, payload)
+    else:
+        assert await search_function(settings, payload)
+
+    header = "x-api-key" if provider == "exa" else "Authorization"
</code_context>
<issue_to_address>
**Wrong success result passes**

When a retry returns a nonempty but incorrect value, or a string containing “Example” that is not the expected result, `test_search_key_errors_try_next_key` accepts any truthy result at line 1837, and `test_deepseek_key_errors_try_next_key` accepts any string containing “Example” at line 1950; a bogus fallback or error string therefore passes despite the second-key result being wrong.

Assert the expected result from the mocked successful response, rather than only truthiness or a substring.

Also at `tests/unit/test_web_search_tools.py:1950`.
</issue_to_address>