Use StageController for runtime prerendering (#89972)
Stacked on #89971
This controller was introduced to help with dev time validation. It
models stage transitions in a helpful way that will become more useful
soon as we get more advanced with what kinds of sync IO are considered
errors.
To prepare for this we will update the implementation to use the stage
controller for build and runtime prerendering not just dev
We don't yet use it for static prerendering because that one is so
simple and there is really no stage beyond the first one and then an
abort so we will keep it as is
Additionally, the private cache store no longer has the
`runtimeStagePromise`. when you first enter this store type during a
runtime prerender we wait until the outer store's runtime stage has
begun. Previously the proimse signifying this stage transition was
included in the private cache store itself so nested caches could
similarly wait, however you can't actually get to a nested cache until
after it is resolved b/c the outermost one blocks.
