Update client connections guide

`docs/how-to/manage-client-connections.md`

This guide needs a general review and structural redesign. In particular:

- [ ] Decide whether to consistently use `data-integrator` or generic ``
- [ ] Significantly clarify instructions regarding sharded clusters - particularly with regards to users and relations (see [this comment](https://github.com/canonical/mongo-single-kernel-library/pull/95/files#r2401280579))
- [ ] Remove `## Internal operator user` section

Review docs/how-to/manage-client-connections.md first, then read the referenced comment on PR 95 for the sharded-cluster context. Decide on consistent terminology, clarify users and relations for sharded clusters, and remove the Internal operator user section; the guide is done when its structure and instructions are coherent throughout.

Written by the indexing model from the issue text.