try

deploy_remote.yml

@@ -49,12 +49,18 @@
         recreate: always
       register: compose_output
 
+    - name: Get container info
+      community.docker.docker_container_info:
+        name:
+          - "{{ project_name }}-web-1"
+          - "{{ project_name }}-db-1"
+      register: container_info
+
     - name: Verify that web and db services are running
       ansible.builtin.assert:
         that:
-          - '"movie-db-web" in compose_output.services'
-          - 'compose_output.services["movie-db-web"].state == "running"'
-          - '"movie-db-db" in compose_output.services'
-          - 'compose_output.services["movie-db-db"].state == "running"'
+          - container_info.containers is defined
+          - (container_info.containers | selectattr('name', 'equalto', '{{ project_name }}-web-1') | first).State.Running
+          - (container_info.containers | selectattr('name', 'equalto', '{{ project_name }}-db-1') | first).State.Running