perf(ci): optimize latex caching

Signed-off-by: skjnldsv <skjnldsv@protonmail.com>

Author: skjnldsv

.github/workflows/sphinxbuild.yml

@@ -34,6 +34,7 @@ jobs:
           restore-keys: |
             latex-apt-${{ runner.os }}-${{ runner.arch }}-ubuntu-24.04-
             latex-apt-${{ runner.os }}-${{ runner.arch }}-
+          lookup-only: true
 
       - name: Download LaTeX packages (cache miss only)
         if: steps.cache-latex-apt.outputs.cache-hit != 'true'
@@ -47,6 +48,13 @@ jobs:
           # Ensure downloaded packages are owned by the current user so they can be cached
           sudo chown -R $(id -u):$(id -g) ${{ runner.temp }}/.cache/archives
 
+      - name: Save LaTeX apt cache (cache miss only)
+        if: steps.cache-latex-apt.outputs.cache-hit != 'true'
+        uses: actions/cache/save@668228422ae6a00e4ad889ee87cd7109ec5666a7 # v5.0.4
+        with:
+          path: ${{ runner.temp }}/.cache/archives
+          key: latex-apt-${{ runner.os }}-${{ runner.arch }}-ubuntu-24.04-texlive-2023
+
   build:
     name: Build ${{ matrix.manual.name }}
     runs-on: ubuntu-latest