docs: improve pydantic integration docs (#2136)

Address usage mistakes in
https://github.com/lancedb/lancedb/issues/2135.

* Add example of how to use `LanceModel` and `Vector` decorator
* Add test for pydantic doc
* Fix the example to directly use LanceModel instead of calling
`MyModel.to_arrow_schema()` in the example.
* Add cross-reference link to pydantic doc site
* Configure mkdocs to watch code changes in python directory.

python/python/tests/docs/test_pydantic_integration.py

@@ -0,0 +1,36 @@
+# SPDX-License-Identifier: Apache-2.0
+# SPDX-FileCopyrightText: Copyright The LanceDB Authors
+
+# --8<-- [start:imports]
+import lancedb
+from lancedb.pydantic import Vector, LanceModel
+# --8<-- [end:imports]
+
+
+def test_pydantic_model(tmp_path):
+    # --8<-- [start:base_model]
+    class PersonModel(LanceModel):
+        name: str
+        age: int
+        vector: Vector(2)
+
+    # --8<-- [end:base_model]
+
+    # --8<-- [start:set_url]
+    url = "./example"
+    # --8<-- [end:set_url]
+    url = tmp_path
+
+    # --8<-- [start:base_example]
+    db = lancedb.connect(url)
+    table = db.create_table("person", schema=PersonModel)
+    table.add(
+        [
+            PersonModel(name="bob", age=1, vector=[1.0, 2.0]),
+            PersonModel(name="alice", age=2, vector=[3.0, 4.0]),
+        ]
+    )
+    assert table.count_rows() == 2
+    person = table.search([0.0, 0.0]).limit(1).to_pydantic(PersonModel)
+    assert person[0].name == "bob"
+    # --8<-- [end:base_example]