[SPARK-49861][INFRA] Add Python 3.13 to Infra docker image

dev/infra/Dockerfile

@@ -142,6 +142,16 @@ RUN python3.12 -m pip install $BASIC_PIP_PKGS $CONNECT_PIP_PKGS lxml && \
     python3.12 -m pip install torcheval && \
     python3.12 -m pip cache purge
 
+# Install Python 3.13 at the last stage to avoid breaking the existing Python installations
+RUN apt-get update && apt-get install -y \
+    python3.13 \
+    && rm -rf /var/lib/apt/lists/*
+RUN curl -sS https://bootstrap.pypa.io/get-pip.py | python3.13
+# TODO(SPARK-49862) Add BASIC_PIP_PKGS and CONNECT_PIP_PKGS to Python 3.13 image when it supports Python 3.13
+RUN python3.13 -m pip install --ignore-installed blinker>=1.6.2 # mlflow needs this
+RUN python3.13 -m pip install unittest-xml-reporting lxml && \
+    python3.13 -m pip cache purge
+
 # Remove unused installation packages to free up disk space
 RUN apt-get remove --purge -y 'gfortran-11' 'humanity-icon-theme' 'nodejs-doc' || true
 RUN apt-get autoremove --purge -y