fix(python): clarify bare Vector annotations (#3809)

## Summary

- raise a clear `TypeError` when `Vector` is used without a dimension
- preserve normal `Vector(dim)` behavior across Pydantic v1 and v2
- add a regression test that defines a model without importing PyArrow

## Root cause

Pydantic interpreted the bare `Vector` factory as a callable field type
and inspected its postponed annotations in the user model's namespace.
Because that namespace did not define LanceDB's internal `pa` alias,
model construction failed with the misleading `NameError: name 'pa' is
not defined` instead of explaining that `Vector` must be parameterized.

The factory now exposes Pydantic's v1 and v2 schema hooks and rejects
bare use before signature introspection with guidance to use
`Vector(dim)`.

## Validation

- `uvx --from 'ruff==0.15.20' ruff check .`
- `uvx --from 'ruff==0.15.20' ruff format --check
python/python/lancedb/pydantic.py python/python/tests/test_pydantic.py`
- `cd python && uv run --extra tests pytest
python/tests/test_pydantic.py::test_bare_vector_raises_clear_error -q`
- `cd python && uv run --extra tests pytest
python/tests/test_pydantic.py -q`
- compatibility checks with Pydantic 1.10.22, 2.11.4, and 2.13.4

Fixes #2384

<!-- lance-gatekeeper-fix:v1 agent=71e7473e18c91db5137a3c0d3bb73640
generation=1 -->

Co-authored-by: Gatefixer <313497061+lancedb-gatefixer[bot]@users.noreply.github.com>

python/python/lancedb/pydantic.py

@@ -153,6 +153,16 @@ def Vector(
     return FixedSizeList
 
 
+def _raise_bare_vector_error(*_args):
+    raise TypeError("Vector must be parameterized with a dimension, e.g. Vector(128).")
+
+
+# Pydantic v1 and v2 otherwise treat the bare Vector factory as a field validator
+# and inspect its signature, which produces misleading errors about internal types.
+setattr(Vector, "__get_validators__", _raise_bare_vector_error)
+setattr(Vector, "__get_pydantic_core_schema__", _raise_bare_vector_error)
+
+
 def MultiVector(
     dim: int, value_type: pa.DataType = pa.float32(), nullable: bool = True
 ) -> Type:

python/python/tests/test_pydantic.py

@@ -415,6 +415,17 @@ def test_nullable_vector():
     assert schema == pa.schema([pa.field("vec", pa.list_(pa.float32(), 16), True)])
 
 
+def test_bare_vector_raises_clear_error():
+    namespace = {
+        "__name__": "test_model_without_pyarrow",
+        "LanceModel": LanceModel,
+        "Vector": Vector,
+    }
+
+    with pytest.raises(TypeError, match=r"Vector must be parameterized.*Vector\(128\)"):
+        exec("class TestModel(LanceModel):\n    vector: Vector", namespace)
+
+
 def test_fixed_size_list_field():
     class TestModel(pydantic.BaseModel):
         vec: Vector(16)