This commit simplifies/systemizes accessing the `CacheStorage` through a
wrapper, with the following benefits:
- Ensuring a consistent cache name prefix is used for all caches
(without having to repeat the prefix in different places).
- Allowing referring to caches using their name without the common
cache name prefix.
- Exposing the cache name on cache instances, which for example makes it
easier to delete caches without having to keep track of the name used
to create them.
PR Close#42622