Continuation of #10632. The `apiBasePath` property in the Search Plugin
config is unnecessary. This plugin reads directly from the Payload
config for this property. Exposing it to the plugin's config was likely
a mistake during sanitization before passing it through to the remaining
files. This property was added to resolve the types, but as result,
exposed it to the config unnecessarily. This PR marks this property with
the deprecated flag to prevent breaking changes.
4a4e90a170