Stabilise long-running state store committer

### Description / Background

We introduced an experimental long-running state store committer in the following issue:
- https://github.com/gchq/sleeper/issues/5091

We'd like to stabilise it so that we would no longer consider it experimental.

### Technical Notes / Implementation Details

See sub-issues.

Start by reading issue #5091 to understand the experimental long-running state store committer, then review the sub-issues linked from this issue. Use those sub-issues to identify the required stabilization work; done means the committer is no longer considered experimental.

Written by the indexing model from the issue text.