diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 5242dfc06f9..0cf849f2a97 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -103,20 +103,9 @@ jobs:
           MAKE: make -j2 --output-sync=recurse
           SAGE_NUM_THREADS: 2
 
-      - name: Set up node to install pyright
-        if: always() && steps.worktree.outcome == 'success'
-        uses: actions/setup-node@v3
-        with:
-          node-version: '12'
-
-      - name: Install pyright
-        if: always() && steps.worktree.outcome == 'success'
-        # Fix to v232 due to bug https://github.com/microsoft/pyright/issues/3239
-        run: npm install -g pyright@1.1.232
-
       - name: Static code check with pyright
         if: always() && steps.worktree.outcome == 'success'
-        run: pyright
+        run: ./sage -tox -e pyright
         working-directory: ./worktree-image
 
       - name: Clean (fallback to non-incremental)
diff --git a/pyrightconfig.json b/pyrightconfig.json
index 643c56360c9..ebf40ea028c 100644
--- a/pyrightconfig.json
+++ b/pyrightconfig.json
@@ -22,4 +22,7 @@
     "reportUndefinedVariable": "warning",
     "reportOptionalOperand": "warning",
     "reportMissingImports": "warning",
+    "reportPrivateImportUsage": "warning",
+    // Suppress because it flags our standard pattern @staticmethod __classcall__(cls, ...)
+    "reportSelfClsParameterName": "none",
 }
diff --git a/src/sage/misc/lazy_attribute.pyi b/src/sage/misc/lazy_attribute.pyi
new file mode 100644
index 00000000000..6a174a37aa2
--- /dev/null
+++ b/src/sage/misc/lazy_attribute.pyi
@@ -0,0 +1,9 @@
+# This type-stub file helps pyright understand the decorator @lazy_attribute.
+
+# Adapted from https://github.com/python/typeshed/blob/b9640005eb586afdbe0a57bac2b88a7a12465069/stdlib/builtins.pyi#L1237-L1254
+class lazy_attribute:
+    def __init__(
+        self,
+        f: Callable[[Any], Any] | None = ...
+    ) -> None: ...
+    def __get__(self, a: Any, cls: type) -> Any: ...
diff --git a/src/sage/schemes/toric/variety.py b/src/sage/schemes/toric/variety.py
index 82d2ec7769a..c2aea308b9b 100644
--- a/src/sage/schemes/toric/variety.py
+++ b/src/sage/schemes/toric/variety.py
@@ -2250,20 +2250,21 @@ def Todd_class(self, deg=None):
             1
         """
         Td = QQ.one()
-        if self.dimension() >= 1:
+        dim = self.dimension()
+        if dim >= 1:
             c1 = self.Chern_class(1)
             Td += QQ.one() / 2 * c1
-        if self.dimension() >= 2:
-            c2 = self.Chern_class(2)
-            Td += QQ.one() / 12 * (c1**2 + c2)
-        if self.dimension() >= 3:
-            Td += QQ.one() / 24 * c1*c2
-        if self.dimension() >= 4:
-            c3 = self.Chern_class(3)
-            c4 = self.Chern_class(4)
-            Td += -QQ.one() / 720 * (c1**4 - 4*c1**2*c2 - 3*c2**2 - c1*c3 + c4)
-        if self.dimension() >= 5:
-            raise NotImplementedError('Todd class is currently only implemented up to degree 4')
+            if dim >= 2:
+                c2 = self.Chern_class(2)
+                Td += QQ.one() / 12 * (c1**2 + c2)
+                if dim >= 3:
+                    Td += QQ.one() / 24 * c1*c2
+                    if dim >= 4:
+                        c3 = self.Chern_class(3)
+                        c4 = self.Chern_class(4)
+                        Td += -QQ.one() / 720 * (c1**4 - 4*c1**2*c2 - 3*c2**2 - c1*c3 + c4)
+                        if dim >= 5:
+                            raise NotImplementedError('Todd class is currently only implemented up to degree 4')
         if deg is None:
             return Td
         else:
diff --git a/src/tox.ini b/src/tox.ini
index fea30bea362..e6c9bfccdcc 100644
--- a/src/tox.ini
+++ b/src/tox.ini
@@ -78,21 +78,22 @@ commands =
 [testenv:pyright]
 description =
     run the static typing checker pyright
-deps = pyright
+deps =
+    pyright
 setenv =
     {[sagedirect]setenv}
     HOME={envdir}
-    # Fix version, see .github/workflows/build.yml
-    PYRIGHT_PYTHON_FORCE_VERSION=1.1.232
+    PYRIGHT_PYTHON_FORCE_VERSION=1.1.332
+    PYRIGHT_PYTHON_GLOBAL_NODE=false
+    NODE_OPTIONS=--max-old-space-size=8192
 allowlist_externals = {[sagedirect]allowlist_externals}
 ## We run pyright from within the sage-env so that SAGE_LOCAL is available.
 ## pyright is already configured via SAGE_ROOT/pyrightconfig.json to use our venv.
 ##
-## Running pyright on the whole Sage source tree takes very long
-## and may run out of memory. When no files/directories are given, just run it
-## on the packages that already have typing annotations.
+## Note that running pyright on the whole Sage source tree (= default) takes very long
+## and may run out of memory.
 commands =
-    {env:SAGE} -sh -c 'pyright {posargs:{toxinidir}/sage/combinat {toxinidir}/sage/manifolds}'
+    {env:SAGE} -sh -c 'pyright {posargs:}'
 
 [testenv:pycodestyle]
 description =