feat: record load balancing primary LSN on writes

mentioned in commit 09a142a8

mentioned in issue #1368 (closed)

mentioned in merge request gitlab-org/charts/gitlab!3938 (merged)

mentioned in merge request omnibus-gitlab!7965 (merged)

mentioned in merge request gitlab-org/build/CNG!2052 (merged)

mentioned in merge request gitlab-com/gl-infra/k8s-workloads/gitlab-com!3903 (merged)

mentioned in merge request gitlab-com/gl-infra/k8s-workloads/gitlab-com!3911 (merged)

mentioned in merge request gitlab-com/gl-infra/k8s-workloads/gitlab-com!3916 (merged)