As of gh-22340, `MimeTypeUtils` has a built-in LRU cache implementation
for caching parsed MIME types and avoiding excessive garbage creation at
runtime.
This implementation, when hit with highly concurrent reads on the same
media type (the cache key), can create multiple keys for the same MIME
type string. This duplication leads to the cache filling up and evicting
entries. When the cache fetches a duplicate key, it is then not
associated with a value and the cache can return a `null` value, which
is forbidden by the API contract.
This commit adds another cache check within the write lock: this avoids
creating duplicate entries in the cache and `null` return values.
Fixes gh-23211