Before when a value was copied to a field through a parent field or `copy_to`,
we parsed it using the `FieldMapper` from the source field. Instead we should
parse it using the target `FieldMapper`. This ensures that we apply the
appropriate mapping type and options to the copied value.
To implement the fix cleanly, this PR refactors the value parsing strategy. Now
instead of looking up values directly, field mappers produce a helper object
`ValueFetcher`. The value fetchers are responsible for almost all aspects of
fetching, including looking up the right paths in the _source.
The PR is fairly big but each commit can be reviewed individually.
Fixes#61033.
997c73ec17