fix: Python 3.13t with GIL (#5139)

* ci: try Python 3.13t

Signed-off-by: Henry Schreiner <henryschreineriii@gmail.com>

* fix: support Python 3.13t

Signed-off-by: Henry Schreiner <henryschreineriii@gmail.com>

* fix: patch PyPy

Signed-off-by: Henry Schreiner <henryschreineriii@gmail.com>

* tests: one more int cast

Signed-off-by: Henry Schreiner <henryschreineriii@gmail.com>

* tests: cleanup

Signed-off-by: Henry Schreiner <henryschreineriii@gmail.com>

* refactor: use named constant in tests for immortal refcounts

Signed-off-by: Henry Schreiner <henryschreineriii@gmail.com>

* docs: move comment about free threaded Python

Signed-off-by: Henry Schreiner <henryschreineriii@gmail.com>

---------

Signed-off-by: Henry Schreiner <henryschreineriii@gmail.com>

.github/workflows/ci.yml

@@ -196,6 +196,35 @@ jobs:
         pytest tests/extra_setuptools
       if: "!(matrix.runs-on == 'windows-2022')"
 
+  manylinux:
+    name: Manylinux on 🐍 3.13t • GIL
+    runs-on: ubuntu-latest
+    timeout-minutes: 40
+    container: quay.io/pypa/musllinux_1_2_x86_64:latest
+    steps:
+      - uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+
+      - name: Prepare venv
+        run: python3.13 -m venv .venv
+
+      - name: Install Python deps
+        run: .venv/bin/pip install -r tests/requirements.txt
+
+      - name: Configure C++11
+        run: >
+          cmake -S. -Bbuild
+          -DPYBIND11_WERROR=ON
+          -DDOWNLOAD_CATCH=ON
+          -DDOWNLOAD_EIGEN=ON
+          -DPython_ROOT_DIR=.venv
+
+      - name: Build C++11
+        run: cmake --build build -j2
+
+      - name: Python tests C++11
+        run: cmake --build build --target pytest -j2
 
   deadsnakes:
     strategy: