ci: Adapt to updated release module template

The release module moved into production now. The process changed
slightly with regard to the testing period, so we will have to
adapt the existing job a bit.

Part-of: <https://gitlab.gnome.org/GNOME/gnome-shell-extensions/-/merge_requests/367>
(cherry picked from commit 5d8d3601b4)

.gitlab-ci.yml

@@ -5,8 +5,11 @@
 include:
   - remote: 'https://gitlab.freedesktop.org/freedesktop/ci-templates/-/raw/bbe5232986c9b98eb1efe62484e07216f7d1a4df/templates/fedora.yml'
   - remote: "https://gitlab.freedesktop.org/freedesktop/ci-templates/-/raw/6f86b8bcb0cd5168c32779c4fea9a893c4a0c046/templates/ci-fairy.yml"
-  - project: 'Infrastructure/openshift-images/gnome-release-service'
-    file: '/ci-templates/release-module.yml'
+  - component: gitlab.gnome.org/GNOME/citemplates/release-service@master
+    inputs:
+      job-stage: deploy
+      dist-job-name: fedora-dist-tarball
+      tarball-artifact-path: "$TARBALL_ARTIFACT_PATH"
 
 stages:
   - pre_review
@@ -31,6 +34,7 @@ default:
 variables:
   FDO_UPSTREAM_REPO: GNOME/gnome-shell-extensions
   MESON_BUILD_DIR: build
+  TARBALL_ARTIFACT_PATH: "${MESON_BUILD_DIR}/meson-dist/${CI_PROJECT_NAME}-${CI_COMMIT_TAG}.tar.xz"
 
 workflow:
   rules:
@@ -169,15 +173,9 @@ fedora-dist-tarball:
   extends: fedora-dist
   artifacts:
     expose_as: 'Get tarball here'
+    name: "${CI_JOB_NAME}-${CI_COMMIT_REF_NAME}"
+    when: always
     paths:
-      - "${MESON_BUILD_DIR}/meson-dist/${CI_PROJECT_NAME}-${CI_COMMIT_TAG}.tar.xz"
-  rules:
-    - if: '$CI_COMMIT_TAG'
-
-release-module:
-  stage: deploy
-  needs:
-    - fedora-dist-tarball
-  extends: .release-module
+      - "$TARBALL_ARTIFACT_PATH"
   rules:
     - if: '$CI_COMMIT_TAG'