Fixing database backup rake task in single-db-two-connections mode

What does this MR do and why?

Extracting a fix from this MR: !112731 (merged)

In !112731 (merged) we are adding tests coverage for the new database setup mode, which is single-db-ci-connection. Where GitLab connects to a Single Database, but through two different set of connection pool. One for gitlab_main tables, and one for gitlab_ci.

While working on that MR, we discovered an issue with the backup rake task. When running in this mode single-db-ci-connection, it backups the same (only) database twice.

This MR extracts the fix into its own separate MR, based on this comment

How to set up and validate locally

1. Make sure you are running in single-db-ci-connection mode. Your config/database.yml should look like

development:
  main: &development_main
    adapter: postgresql
    encoding: unicode
    database: gitlabhq_development
  ci:
    adapter: postgresql
    encoding: unicode
    database: gitlabhq_development # this should be the same database name as in main
    database_tasks: false # This is important

2. On the master branch, run this command

rake gitlab:backup:create SKIP=repositories,builds,artifacts,pages,lfs,terraform_state,registry,packages

It will generate a newly compressed file in the tmp/backups folder. If you list the files inside this file, using the command

tar --list -f tmp/backups/1679331599_2023_03_20_15.10.0-pre_gitlab_backup.tar

You will get

backup_information.yml
db/
db/ci_database.sql.gz # This should not be there
db/database.sql.gz
uploads.tar.gz

3. On this branch, you should get the following instead

backup_information.yml
db/
db/database.sql.gz
uploads.tar.gz

MR acceptance checklist

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Related to #391646 (closed)