To address #23862 , #23851 removes an inheritance, which affects a fairly large number of call-sites.

To make #23851 reviewable, a horrible implicit cast operator Scope& was added to Stats::Store. This keeps keeps a lot of noisy changes out of that PR, but leaves behind tech-debt. This bug tracks that tech-debt, which should be resolvable in a huge PR with no semantic changes, after #23851 lands.