[doc] Update release playbook for recent changes (#21359)

Staging builds recently switched from being Bazel-driven to
CMake-driven. Update the release playbook accordingly.

doc/_pages/release_playbook.md

@@ -110,8 +110,8 @@ the main body of the document:
       has nothing still running (modulo the ``*-coverage`` builds, which we can
       ignore)
    3. Open the latest builds from the following builds:
-      1. <https://drake-jenkins.csail.mit.edu/view/Packaging/job/linux-jammy-unprovisioned-gcc-bazel-nightly-packaging/>
-      2. <https://drake-jenkins.csail.mit.edu/view/Packaging/job/mac-arm-ventura-unprovisioned-clang-bazel-nightly-packaging/>
+      1. <https://drake-jenkins.csail.mit.edu/view/Packaging/job/linux-jammy-unprovisioned-gcc-cmake-nightly-packaging/>
+      2. <https://drake-jenkins.csail.mit.edu/view/Packaging/job/mac-arm-ventura-unprovisioned-clang-cmake-nightly-packaging/>
    4. Check the logs for those packaging builds and find the URLs they posted
       to (open the latest build, go to "View as plain text", and search for
       ``drake/nightly/drake-20``), and find the date.  It will be ``YYYYMMDD``
@@ -128,8 +128,8 @@ the main body of the document:
       new browser tab):
       - [Linux Wheel Staging](https://drake-jenkins.csail.mit.edu/view/Staging/job/linux-jammy-unprovisioned-gcc-wheel-staging-release/)
       - [macOS arm Wheel Staging](https://drake-jenkins.csail.mit.edu/view/Staging/job/mac-arm-ventura-unprovisioned-clang-wheel-staging-release/)
-      - [Jammy Packaging Staging](https://drake-jenkins.csail.mit.edu/view/Staging/job/linux-jammy-unprovisioned-gcc-bazel-staging-packaging/)
-      - [macOS arm Packaging Staging](https://drake-jenkins.csail.mit.edu/view/Staging/job/mac-arm-ventura-unprovisioned-clang-bazel-staging-packaging/)
+      - [Jammy Packaging Staging](https://drake-jenkins.csail.mit.edu/view/Staging/job/linux-jammy-unprovisioned-gcc-cmake-staging-packaging/)
+      - [macOS arm Packaging Staging](https://drake-jenkins.csail.mit.edu/view/Staging/job/mac-arm-ventura-unprovisioned-clang-cmake-staging-packaging/)
    2. In the upper right, click "log in" (unless you're already logged in). This
       will use your GitHub credentials.
    3. Click "Build with Parameters".