diff --git a/.github/workflows/ci-additional.yaml b/.github/workflows/ci-additional.yaml
index e2685f445d7..ff3e8ab7e63 100644
--- a/.github/workflows/ci-additional.yaml
+++ b/.github/workflows/ci-additional.yaml
@@ -105,11 +105,9 @@ jobs:
         run: |
           python -m pip install mypy
 
-      # Temporarily overriding to be true due to https://github.com/pydata/xarray/issues/6551
-      # python -m mypy --install-types --non-interactive
       - name: Run mypy
         run: |
-          python -m mypy --install-types --non-interactive || true
+          python -m mypy --install-types --non-interactive
 
   min-version-policy:
     name: Minimum Version Policy
diff --git a/xarray/backends/api.py b/xarray/backends/api.py
index 9967b0a08c0..4962a4a9c02 100644
--- a/xarray/backends/api.py
+++ b/xarray/backends/api.py
@@ -35,7 +35,7 @@
     try:
         from dask.delayed import Delayed
     except ImportError:
-        Delayed = None
+        Delayed = None  # type: ignore
 
 
 DATAARRAY_NAME = "__xarray_dataarray_name__"
diff --git a/xarray/backends/locks.py b/xarray/backends/locks.py
index 59417336f5f..1cc93779843 100644
--- a/xarray/backends/locks.py
+++ b/xarray/backends/locks.py
@@ -7,12 +7,12 @@
     from dask.utils import SerializableLock
 except ImportError:
     # no need to worry about serializing the lock
-    SerializableLock = threading.Lock
+    SerializableLock = threading.Lock  # type: ignore
 
 try:
     from dask.distributed import Lock as DistributedLock
 except ImportError:
-    DistributedLock = None
+    DistributedLock = None  # type: ignore
 
 
 # Locks used by multiple backends.
diff --git a/xarray/core/_typed_ops.pyi b/xarray/core/_typed_ops.pyi
index e23b5848ff7..e5b3c9112c7 100644
--- a/xarray/core/_typed_ops.pyi
+++ b/xarray/core/_typed_ops.pyi
@@ -21,7 +21,7 @@ from .variable import Variable
 try:
     from dask.array import Array as DaskArray
 except ImportError:
-    DaskArray = np.ndarray
+    DaskArray = np.ndarray  # type: ignore
 
 # DatasetOpsMixin etc. are parent classes of Dataset etc.
 # Because of https://github.com/pydata/xarray/issues/5755, we redefine these. Generally
diff --git a/xarray/core/computation.py b/xarray/core/computation.py
index 1a32cda512c..6f1e08bf84f 100644
--- a/xarray/core/computation.py
+++ b/xarray/core/computation.py
@@ -17,7 +17,6 @@
     Iterable,
     Mapping,
     Sequence,
-    overload,
 )
 
 import numpy as np
@@ -1846,24 +1845,26 @@ def where(cond, x, y, keep_attrs=None):
     )
 
 
-@overload
-def polyval(coord: DataArray, coeffs: DataArray, degree_dim: Hashable) -> DataArray:
-    ...
+# These overloads seem not to work — mypy says it can't find a matching overload for
+# `DataArray` & `DataArray`, despite that being in the first overload. Would be nice to
+# have overloaded functions rather than just `T_Xarray` for everything.
 
+# @overload
+# def polyval(coord: DataArray, coeffs: DataArray, degree_dim: Hashable) -> DataArray:
+#     ...
 
-@overload
-def polyval(coord: T_Xarray, coeffs: Dataset, degree_dim: Hashable) -> Dataset:
-    ...
 
+# @overload
+# def polyval(coord: T_Xarray, coeffs: Dataset, degree_dim: Hashable) -> Dataset:
+#     ...
 
-@overload
-def polyval(coord: Dataset, coeffs: T_Xarray, degree_dim: Hashable) -> Dataset:
-    ...
+
+# @overload
+# def polyval(coord: Dataset, coeffs: T_Xarray, degree_dim: Hashable) -> Dataset:
+#     ...
 
 
-def polyval(
-    coord: T_Xarray, coeffs: T_Xarray, degree_dim: Hashable = "degree"
-) -> T_Xarray:
+def polyval(coord: T_Xarray, coeffs: T_Xarray, degree_dim="degree") -> T_Xarray:
     """Evaluate a polynomial at specific values
 
     Parameters
diff --git a/xarray/core/dask_array_compat.py b/xarray/core/dask_array_compat.py
index 4d73867a283..e114c238b72 100644
--- a/xarray/core/dask_array_compat.py
+++ b/xarray/core/dask_array_compat.py
@@ -5,7 +5,7 @@
 try:
     import dask.array as da
 except ImportError:
-    da = None
+    da = None  # type: ignore
 
 
 def _validate_pad_output_shape(input_shape, pad_width, output_shape):
diff --git a/xarray/core/dataarray.py b/xarray/core/dataarray.py
index d15cbd00c0d..fc3cbef16f8 100644
--- a/xarray/core/dataarray.py
+++ b/xarray/core/dataarray.py
@@ -17,6 +17,7 @@
 import numpy as np
 import pandas as pd
 
+from ..backends.common import AbstractDataStore, ArrayWriter
 from ..coding.calendar_ops import convert_calendar, interp_calendar
 from ..coding.cftimeindex import CFTimeIndex
 from ..plot.plot import _PlotMethods
@@ -67,7 +68,7 @@
     try:
         from dask.delayed import Delayed
     except ImportError:
-        Delayed = None
+        Delayed = None  # type: ignore
     try:
         from cdms2 import Variable as cdms2_Variable
     except ImportError:
@@ -2875,7 +2876,9 @@ def to_masked_array(self, copy: bool = True) -> np.ma.MaskedArray:
         isnull = pd.isnull(values)
         return np.ma.MaskedArray(data=values, mask=isnull, copy=copy)
 
-    def to_netcdf(self, *args, **kwargs) -> bytes | Delayed | None:
+    def to_netcdf(
+        self, *args, **kwargs
+    ) -> tuple[ArrayWriter, AbstractDataStore] | bytes | Delayed | None:
         """Write DataArray contents to a netCDF file.
 
         All parameters are passed directly to :py:meth:`xarray.Dataset.to_netcdf`.
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 76776b4bc44..1166e240120 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -32,6 +32,7 @@
 
 import xarray as xr
 
+from ..backends.common import ArrayWriter
 from ..coding.calendar_ops import convert_calendar, interp_calendar
 from ..coding.cftimeindex import CFTimeIndex, _parse_array_of_cftime_strings
 from ..plot.dataset_plot import _Dataset_PlotMethods
@@ -110,7 +111,7 @@
     try:
         from dask.delayed import Delayed
     except ImportError:
-        Delayed = None
+        Delayed = None  # type: ignore
 
 
 # list of attributes of pd.DatetimeIndex that are ndarrays of time info
@@ -1686,7 +1687,7 @@ def to_netcdf(
         unlimited_dims: Iterable[Hashable] = None,
         compute: bool = True,
         invalid_netcdf: bool = False,
-    ) -> bytes | Delayed | None:
+    ) -> tuple[ArrayWriter, AbstractDataStore] | bytes | Delayed | None:
         """Write dataset contents to a netCDF file.
 
         Parameters
diff --git a/xarray/core/duck_array_ops.py b/xarray/core/duck_array_ops.py
index b85d0e1645e..253a68b7205 100644
--- a/xarray/core/duck_array_ops.py
+++ b/xarray/core/duck_array_ops.py
@@ -30,7 +30,7 @@
     import dask.array as dask_array
     from dask.base import tokenize
 except ImportError:
-    dask_array = None
+    dask_array = None  # type: ignore
 
 
 def _dask_or_eager_func(
diff --git a/xarray/core/nanops.py b/xarray/core/nanops.py
index c1a4d629f97..fa96bd6e150 100644
--- a/xarray/core/nanops.py
+++ b/xarray/core/nanops.py
@@ -11,7 +11,7 @@
 
     from . import dask_array_compat
 except ImportError:
-    dask_array = None
+    dask_array = None  # type: ignore[assignment]
     dask_array_compat = None  # type: ignore[assignment]
 
 
diff --git a/xarray/core/types.py b/xarray/core/types.py
index 3f368501b25..74cb2fc2d46 100644
--- a/xarray/core/types.py
+++ b/xarray/core/types.py
@@ -16,7 +16,7 @@
     try:
         from dask.array import Array as DaskArray
     except ImportError:
-        DaskArray = np.ndarray
+        DaskArray = np.ndarray  # type: ignore
 
 
 T_Dataset = TypeVar("T_Dataset", bound="Dataset")
diff --git a/xarray/tests/test_computation.py b/xarray/tests/test_computation.py
index 127fdc5404f..c59f1a6584f 100644
--- a/xarray/tests/test_computation.py
+++ b/xarray/tests/test_computation.py
@@ -1,3 +1,5 @@
+from __future__ import annotations
+
 import functools
 import operator
 import pickle
@@ -22,6 +24,7 @@
     unified_dim_sizes,
 )
 from xarray.core.pycompat import dask_version
+from xarray.core.types import T_Xarray
 
 from . import has_dask, raise_if_dask_computes, requires_dask
 
@@ -2009,14 +2012,14 @@ def test_where_attrs() -> None:
         ),
     ],
 )
-def test_polyval(use_dask, x, coeffs, expected) -> None:
+def test_polyval(use_dask, x: T_Xarray, coeffs: T_Xarray, expected) -> None:
     if use_dask:
         if not has_dask:
             pytest.skip("requires dask")
         coeffs = coeffs.chunk({"degree": 2})
         x = x.chunk({"x": 2})
     with raise_if_dask_computes():
-        actual = xr.polyval(x, coeffs)
+        actual = xr.polyval(coord=x, coeffs=coeffs)
     xr.testing.assert_allclose(actual, expected)
 
 
diff --git a/xarray/tests/test_testing.py b/xarray/tests/test_testing.py
index 2bde7529d1e..1470706d0eb 100644
--- a/xarray/tests/test_testing.py
+++ b/xarray/tests/test_testing.py
@@ -10,7 +10,7 @@
 try:
     from dask.array import from_array as dask_from_array
 except ImportError:
-    dask_from_array = lambda x: x
+    dask_from_array = lambda x: x  # type: ignore
 
 try:
     import pint
diff --git a/xarray/util/generate_ops.py b/xarray/util/generate_ops.py
index f1fd6cbfeb2..0a382642708 100644
--- a/xarray/util/generate_ops.py
+++ b/xarray/util/generate_ops.py
@@ -210,7 +210,7 @@ def inplace():
 try:
     from dask.array import Array as DaskArray
 except ImportError:
-    DaskArray = np.ndarray
+    DaskArray = np.ndarray  # type: ignore
 
 # DatasetOpsMixin etc. are parent classes of Dataset etc.
 # Because of https://github.com/pydata/xarray/issues/5755, we redefine these. Generally