Set up Subgroups and projects tab on group overview

What does this MR do and why?

Dependent on !202684 (merged) and !202980 (merged)

Related to #516305 (closed)

We are working to migrate group and project lists to shared Vue components. This will give us consistent UX across the product and help reduce technical debit. Currently we are working on group overview in &13790 (closed). This MR sets up the Subgroups and projects tab. Other tabs will be set up in follow-up MRs/issues.

References

Screenshots or screen recordings

Screen_Recording_2025-08-27_at_10.10.57_AM

How to set up and validate locally

1. Enable groups_overview_shared_vue_components feature flag in /rails/features
2. Go to a group
3. Add a subgroup and project. Add nested subgroups and projects if you would like

MR acceptance checklist

Evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.