PARTIAL SUCCESS: Upgrade Geo multi-server installation from 12.9.10 to 12.10.12
### Versions
Current: `12.9.10`
Target: `12.10.12`
### Upgrade checklist
#### Preflight - upgrade
* [x] Create a zoom meeting and schedule a recorded meeting
* [x] Check if the Geo HA update instructions contain [version specific changes](https://docs.gitlab.com/ee/administration/geo/replication/updating_the_geo_nodes.html#version-specific-update-steps)
* [x] Check if PostgreSQL is already the latest shipped version. If not, ensure PostgreSQL upgrade instructions are followed.
* [x] Check if any [upgrade warnings exist](https://docs.gitlab.com/omnibus/update/#version-specific-changes)
* [x] Verify that the Geo cluster is healthy pre-upgrade. For a no-downtime upgrade, remove deploy nodes from load balancers/stop sidekiq and run looping-pipeline to confirm test pass.
* [x] Find the [latest packaged version](https://packages.gitlab.com/gitlab/gitlab-ee) of GitLab that [can be used for zero downtime upgrades](https://docs.gitlab.com/ee/update/README.html#upgrading-without-downtime )
* [x] Set up the [looping test pipeline](https://gitlab.com/gitlab-org/quality/looping-pipeline) to run during the upgrade procedure.
### Upgrade
* [x] Retrieve a beverage of choice within a drinkable temperature range
* [x] Join Zoom meeting and wait for arrival. Hit the **record** button
* [x] Manually trigger the looping test pipeline to start running smoke tests before upgrading the primary site and before upgrading the secondary site (if failures happen during the primary site update)
* [x] Perform upgrade steps described in [latest documentation](https://docs.gitlab.com/omnibus/update/README.html#multi-node--ha-deployment-with-geo).
* [x] During the upgrade process, monitor the looping test pipeline for any failures
* [x] Record any issues encountered during the upgrade
* [x] Verify cluster health post upgrade
* [x] Verify PostgreSQL version is correct
### Postflight
* [x] Record the upgrade outcome as SUCCESS (upgrade with zero downtime), FAILED, PARTIAL SUCCESS (upgrade but with downtime or unconfirmed downtime)
* [x] Open new issues and inform @nhxnguyen and @fzimmer to confirm next steps
* [x] Create new issue for the next upgrade demo (the next versions) and assign to @nhxnguyen and @fzimmer
* [x] Open an issue/MR to update Geo validation tests docs page (doc/administration/geo/replication/geo_validation_tests.md)
issue