Describe the problem

The backup code uses the stats cache to retrieve table statistics for backup.

As a result, we only back up what the stats cache returns and it doesn't return partial statistics.

While it does return "merged" statistics which at least contains the estimates produce in those statistics, those will be excluded from the backup after #94992.

One option here is to stop using the stats cache for retrieving the statistics and instead create some new, more appropriate API.

Jira issue: CRDB-23298