[VSA] Refactor project-level feature to use group-level code
### Problem to solve
There are 2 implementations of the Value Stream Analytics (VSA) feature:
1. Group-level
1. Project-level
In recent months these 2 implementations have begun to diverge substantially, because we have invested in refactoring ([example](https://gitlab.com/gitlab-org/gitlab/merge_requests/16775/diffs#6c1aff793e288e33581de3369f333b8aa888428f_0_38)) and enhancing the group-level implementation, but not the project-level. Basically we have 2 different features now. That is a problem because:
- [Different values displayed between the 2 features](https://gitlab.com/gitlab-org/gitlab/-/issues/213029).
- Increased cost of maintaining 2 separate features.
- Unable to offer cool group-level features (like custom stages) at the project level (per https://gitlab.com/gitlab-org/gitlab/-/issues/30079#note_357374957)
### Further details
The ~"group::analytics" [has discussed](https://gitlab.com/gitlab-org/gitlab/-/issues/30079#note_315668874) whether to 1) move FOSS functionality to the group-level and delete the project-level (gitlab#30079) or 2) refactor the project-level to use the new group-level code (this issue). It has been estimated that the [effort would be about the same](https://gitlab.com/gitlab-org/gitlab/-/issues/213029#note_316012604) between these approaches.
### Proposal
Refactor project-level VSA to use the group-level code:
- [x] [Migrate project-level VSA to use group-level backend](https://gitlab.com/gitlab-org/gitlab/-/issues/213029) gitlab~2492649
- [x] [Eliminate un-used Cycle Analytics code for legacy version](https://gitlab.com/gitlab-org/gitlab/-/issues/292730) gitlab~2492649
- [x] [Add vuex store](https://gitlab.com/gitlab-org/gitlab/-/issues/257828)
- [x] [Migrate the project-level navigation to the path navigation layout](https://gitlab.com/gitlab-org/gitlab/-/issues/326695)
- [x] [Update project-level stage median requests](https://gitlab.com/gitlab-org/gitlab/-/issues/257830)
- [x] [Migrate project level stage table to the new layout](https://gitlab.com/gitlab-org/gitlab/-/issues/326704)
- [x] [Migrate project level stage (records) endpoint](https://gitlab.com/gitlab-org/gitlab/-/issues/336864)
- [x] [Migrate the project level filters to use the group level filter bar](https://gitlab.com/gitlab-org/gitlab/-/issues/326701)#
- [x] [Introduce a default value stream](https://gitlab.com/gitlab-org/gitlab/-/issues/326705)
- [x] [Update project level metrics](https://gitlab.com/gitlab-org/gitlab/-/issues/327435)
- [x] [Add deep linking for query parameters](https://gitlab.com/gitlab-org/gitlab/-/issues/327457)
- [x] [[VSA][FE] Add sorting and pagination to the project level stage table](https://gitlab.com/gitlab-org/gitlab/-/issues/335974)
- [x] [VSA Exclude stages a user does not have permissions for](https://gitlab.com/gitlab-org/gitlab/-/issues/335810) ~backend ~frontend
Note: This is a tracking issue, not an implementation issue.
### Moved to https://gitlab.com/groups/gitlab-org/-/epics/6749
- [Add customizable VSA features](https://gitlab.com/gitlab-org/gitlab/-/issues/326706)
- [Implement the chart data for the default value stream](https://gitlab.com/gitlab-org/gitlab/-/issues
- [Add an overview stage to the project level](https://gitlab.com/gitlab-org/gitlab/-/issues/326700)
### Implementation recommendations
- See the thread starting here: https://gitlab.com/gitlab-org/gitlab/-/issues/30079#note_356967059
epic