diff --git a/.github/workflows/ci_sh_def.yml b/.github/workflows/ci_sh_def.yml
index 2258d238..529b37ec 100644
--- a/.github/workflows/ci_sh_def.yml
+++ b/.github/workflows/ci_sh_def.yml
@@ -43,13 +43,12 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        runs-on: [ubuntu-20.04, windows-2022, macos-latest]
+        runs-on: [ubuntu-20.04, windows-2022, macos-13]
         python:
         - '3.6'
         - '3.9'
-        - '3.10'
-        - '3.11'
         - '3.12'
+        - '3.13'
         - 'pypy-3.8'
         - 'pypy-3.9'
         - 'pypy-3.10'
@@ -77,6 +76,10 @@ jobs:
           # Inject a couple Windows 2019 runs
           - runs-on: windows-2019
             python: '3.9'
+          # Extra ubuntu latest job
+          - runs-on: ubuntu-latest
+            python: '3.11'
+
 
     name: "🐍 ${{ matrix.python }} • ${{ matrix.runs-on }} • x64 ${{ matrix.args }}"
     runs-on: ${{ matrix.runs-on }}
@@ -88,6 +91,7 @@ jobs:
       uses: actions/setup-python@v5
       with:
         python-version: ${{ matrix.python }}
+        allow-prereleases: true
 
     - name: Setup Boost (Linux)
       # Can't use boost + define _
@@ -1000,7 +1004,6 @@ jobs:
           mingw-w64-${{matrix.env}}-cmake
           mingw-w64-${{matrix.env}}-make
           mingw-w64-${{matrix.env}}-python-pytest
-          mingw-w64-${{matrix.env}}-eigen3
           mingw-w64-${{matrix.env}}-boost
           mingw-w64-${{matrix.env}}-catch
 
@@ -1011,6 +1014,7 @@ jobs:
         install: >-
           git
           mingw-w64-${{matrix.env}}-python-scipy
+          mingw-w64-${{matrix.env}}-eigen3
 
     - uses: actions/checkout@v4
 
@@ -1150,8 +1154,8 @@ jobs:
         run: git clean -fdx
 
   macos_brew_install_llvm:
-    name: "macos-latest • brew install llvm"
-    runs-on: macos-latest
+    name: "macos-13 • brew install llvm"
+    runs-on: macos-13
 
     env:
       # https://apple.stackexchange.com/questions/227026/how-to-install-recent-clang-with-homebrew
diff --git a/.github/workflows/ci_sh_def.yml.patch b/.github/workflows/ci_sh_def.yml.patch
index dc83b980..f0cb7f9b 100644
--- a/.github/workflows/ci_sh_def.yml.patch
+++ b/.github/workflows/ci_sh_def.yml.patch
@@ -1,5 +1,5 @@
---- ci.yml	2024-03-27 17:06:50.362431921 -0700
-+++ ci_sh_def.yml	2024-03-27 17:07:41.890376614 -0700
+--- ci.yml	2024-05-26 21:14:20.025983967 -0700
++++ ci_sh_def.yml	2024-05-26 21:14:44.673959335 -0700
 @@ -1,4 +1,16 @@
 -name: CI
 +# PLEASE KEEP THIS GROUP OF FILES IN SYNC AT ALL TIMES:
@@ -27,7 +27,7 @@
    cancel-in-progress: true
  
  env:
-@@ -121,6 +133,7 @@
+@@ -125,6 +137,7 @@
          -DDOWNLOAD_CATCH=ON
          -DDOWNLOAD_EIGEN=ON
          -DCMAKE_CXX_STANDARD=11
@@ -35,7 +35,7 @@
          ${{ matrix.args }}
  
      - name: Build C++11
-@@ -152,6 +165,7 @@
+@@ -156,6 +169,7 @@
          -DDOWNLOAD_CATCH=ON
          -DDOWNLOAD_EIGEN=ON
          -DCMAKE_CXX_STANDARD=17
@@ -43,7 +43,7 @@
          ${{ matrix.args }}
  
      - name: Build
-@@ -173,6 +187,7 @@
+@@ -177,6 +191,7 @@
          -DDOWNLOAD_CATCH=ON
          -DDOWNLOAD_EIGEN=ON
          -DCMAKE_CXX_STANDARD=17
@@ -51,7 +51,7 @@
          -DPYBIND11_INTERNALS_VERSION=10000000
          ${{ matrix.args }}
  
-@@ -260,6 +275,7 @@
+@@ -264,6 +279,7 @@
          -DDOWNLOAD_CATCH=ON
          -DDOWNLOAD_EIGEN=ON
          -DCMAKE_CXX_STANDARD=17
@@ -59,7 +59,7 @@
  
      - name: Build
        run: cmake --build build -j 2
-@@ -328,6 +344,7 @@
+@@ -332,6 +348,7 @@
          -DPYBIND11_WERROR=ON
          -DDOWNLOAD_CATCH=ON
          -DCMAKE_CXX_STANDARD=${{ matrix.std }}
@@ -67,7 +67,7 @@
          -DPYTHON_EXECUTABLE=$(python3 -c "import sys; print(sys.executable)")
  
      - name: Build
-@@ -357,7 +374,7 @@
+@@ -361,7 +378,7 @@
        run: apt-get update && DEBIAN_FRONTEND="noninteractive" apt-get install -y cmake git python3-dev python3-pytest python3-numpy
  
      - name: Configure
@@ -76,7 +76,7 @@
  
      - name: Build
        run: cmake --build build -j2 --verbose
-@@ -445,7 +462,7 @@
+@@ -449,7 +466,7 @@
          cmake -S . -B build -DDOWNLOAD_CATCH=ON \
                              -DCMAKE_CXX_STANDARD=17 \
                              -DPYTHON_EXECUTABLE=$(python3 -c "import sys; print(sys.executable)") \
@@ -85,7 +85,7 @@
                              -DPYBIND11_TEST_FILTER="test_smart_ptr.cpp"
  
      - name: Build
-@@ -499,6 +516,7 @@
+@@ -503,6 +520,7 @@
          -DPYBIND11_WERROR=ON
          -DDOWNLOAD_CATCH=ON
          -DCMAKE_CXX_STANDARD=${{ matrix.std }}
@@ -93,7 +93,7 @@
          -DPYTHON_EXECUTABLE=$(python3 -c "import sys; print(sys.executable)")
  
      - name: Build
-@@ -521,6 +539,7 @@
+@@ -525,6 +543,7 @@
          -DPYBIND11_WERROR=ON
          -DDOWNLOAD_CATCH=ON
          -DCMAKE_CXX_STANDARD=${{ matrix.std }}
@@ -101,7 +101,7 @@
          -DPYTHON_EXECUTABLE=$(python3 -c "import sys; print(sys.executable)")
          "-DPYBIND11_TEST_OVERRIDE=test_call_policies.cpp;test_gil_scoped.cpp;test_thread.cpp"
  
-@@ -570,6 +589,7 @@
+@@ -574,6 +593,7 @@
          -DDOWNLOAD_CATCH=ON     \
          -DDOWNLOAD_EIGEN=OFF    \
          -DCMAKE_CXX_STANDARD=11             \
@@ -109,7 +109,7 @@
          -DCMAKE_CXX_COMPILER=$(which icpc)  \
          -DPYTHON_EXECUTABLE=$(python3 -c "import sys; print(sys.executable)")
  
-@@ -602,6 +622,7 @@
+@@ -606,6 +626,7 @@
          -DDOWNLOAD_CATCH=ON     \
          -DDOWNLOAD_EIGEN=OFF    \
          -DCMAKE_CXX_STANDARD=17             \
@@ -117,7 +117,7 @@
          -DCMAKE_CXX_COMPILER=$(which icpc)  \
          -DPYTHON_EXECUTABLE=$(python3 -c "import sys; print(sys.executable)")
  
-@@ -680,6 +701,7 @@
+@@ -684,6 +705,7 @@
          -DDOWNLOAD_CATCH=ON
          -DDOWNLOAD_EIGEN=ON
          -DCMAKE_CXX_STANDARD=11
@@ -125,7 +125,7 @@
          -DPYTHON_EXECUTABLE=$(python3 -c "import sys; print(sys.executable)")
  
      - name: Build
-@@ -730,6 +752,7 @@
+@@ -734,6 +756,7 @@
          cmake ../pybind11-tests
          -DDOWNLOAD_CATCH=ON
          -DPYBIND11_WERROR=ON
@@ -133,7 +133,7 @@
          -DPYTHON_EXECUTABLE=$(python3 -c "import sys; print(sys.executable)")
        working-directory: /build-tests
  
-@@ -825,6 +848,7 @@
+@@ -829,6 +852,7 @@
          -DPYBIND11_WERROR=ON
          -DDOWNLOAD_CATCH=ON
          -DDOWNLOAD_EIGEN=ON
@@ -141,7 +141,7 @@
          ${{ matrix.args }}
      - name: Build C++11
        run: cmake --build build -j 2
-@@ -879,6 +903,7 @@
+@@ -883,6 +907,7 @@
          -DPYBIND11_WERROR=ON
          -DDOWNLOAD_CATCH=ON
          -DDOWNLOAD_EIGEN=ON
@@ -149,7 +149,7 @@
          ${{ matrix.args }}
      - name: Build C++11
        run: cmake --build build --config Debug -j 2
-@@ -921,6 +946,7 @@
+@@ -925,6 +950,7 @@
          -DDOWNLOAD_CATCH=ON
          -DDOWNLOAD_EIGEN=ON
          -DCMAKE_CXX_STANDARD=20
@@ -157,7 +157,7 @@
  
      - name: Build C++20
        run: cmake --build build -j 2
-@@ -941,6 +967,7 @@
+@@ -945,6 +971,7 @@
          -DDOWNLOAD_CATCH=ON
          -DDOWNLOAD_EIGEN=ON
          -DCMAKE_CXX_STANDARD=20
@@ -165,7 +165,7 @@
          "-DPYBIND11_TEST_OVERRIDE=test_call_policies.cpp;test_gil_scoped.cpp;test_thread.cpp"
  
      - name: Build C++20 - Exercise cmake -DPYBIND11_TEST_OVERRIDE
-@@ -993,6 +1020,7 @@
+@@ -997,6 +1024,7 @@
        run: >-
          cmake -G "MinGW Makefiles" -DCMAKE_CXX_STANDARD=11 -DPYBIND11_WERROR=ON -DDOWNLOAD_CATCH=ON
          -DPYTHON_EXECUTABLE=$(python -c "import sys; print(sys.executable)")
@@ -173,7 +173,7 @@
          -S . -B build
  
      - name: Build C++11
-@@ -1014,6 +1042,7 @@
+@@ -1018,6 +1046,7 @@
        run: >-
          cmake -G "MinGW Makefiles" -DCMAKE_CXX_STANDARD=14 -DPYBIND11_WERROR=ON -DDOWNLOAD_CATCH=ON
          -DPYTHON_EXECUTABLE=$(python -c "import sys; print(sys.executable)")
@@ -181,7 +181,7 @@
          -S . -B build2
  
      - name: Build C++14
-@@ -1035,6 +1064,7 @@
+@@ -1039,6 +1068,7 @@
        run: >-
          cmake -G "MinGW Makefiles" -DCMAKE_CXX_STANDARD=17 -DPYBIND11_WERROR=ON -DDOWNLOAD_CATCH=ON
          -DPYTHON_EXECUTABLE=$(python -c "import sys; print(sys.executable)")
@@ -189,7 +189,7 @@
          -S . -B build3
  
      - name: Build C++17
-@@ -1102,6 +1132,7 @@
+@@ -1106,6 +1136,7 @@
            -DDOWNLOAD_EIGEN=ON
            -DCMAKE_CXX_COMPILER=clang++
            -DCMAKE_CXX_STANDARD=17
@@ -197,7 +197,7 @@
  
        - name: Build
          run: cmake --build . -j 2
-@@ -1167,6 +1198,7 @@
+@@ -1171,6 +1202,7 @@
            -DDOWNLOAD_EIGEN=ON
            -DCMAKE_CXX_COMPILER=clang++
            -DCMAKE_CXX_STANDARD=17
@@ -205,7 +205,7 @@
            -DPYTHON_EXECUTABLE=$(python3 -c "import sys; print(sys.executable)")
  
        - name: Build
-@@ -1190,6 +1222,7 @@
+@@ -1194,6 +1226,7 @@
            -DDOWNLOAD_EIGEN=ON
            -DCMAKE_CXX_COMPILER=clang++
            -DCMAKE_CXX_STANDARD=17