Log MCPServer handler exceptions by kind and keep crash details off the wire (#3314)

Co-authored-by: Marcelo Trylesinski <marcelotryle@gmail.com>

docs/get-started/real-host.md

@@ -6,7 +6,7 @@ Which means connecting to a host is one act: you tell it **the command that star
 
 ## One server, every host
 
-```python title="server.py" hl_lines="3 33-34"
+```python title="server.py" hl_lines="4 34-35"
 --8<-- "docs_src/real_host/tutorial001.py"
 ```
 

docs/get-started/testing.md

@@ -79,8 +79,8 @@ There you go! You can now extend your tests to cover more scenarios.
 Two different things can go wrong, and this flag only touches one of them.
 
 An exception inside one of **your tools** is not a protocol failure. It becomes a normal result with
-`is_error=True`, and the model reads the message. `raise_exceptions` doesn't change that: with or
-without it, `call_tool` returns the same `is_error=True` result. There's a whole page on it:
+`is_error=True` (and if it was a `ToolError`, the model reads your message). `raise_exceptions` doesn't
+change that: with or without it, `call_tool` returns the same `is_error=True` result. There's a whole page on it:
 **[Handling errors](../servers/handling-errors.md)**.
 
 A failure **outside** a tool body is different. On the connection `Client(mcp)` gives you, the