fix(log): use same logger key between both logging packages

mentioned in commit 209cf5f4

mentioned in issue #448 (closed)

mentioned in merge request gitlab-org/build/CNG!757 (merged)

mentioned in merge request gitlab-com/gl-infra/k8s-workloads/gitlab-com!1221 (merged)

mentioned in merge request gitlab-org/charts/gitlab!2181 (merged)

mentioned in merge request gitlab-com/gl-infra/k8s-workloads/gitlab-com!1222 (merged)

mentioned in merge request gitlab-com/gl-infra/k8s-workloads/gitlab-com!1225 (merged)

mentioned in merge request omnibus-gitlab!5600 (merged)

mentioned in merge request gitlab-development-kit!2385 (merged)