TLDR: Generating a Java enum type from an x-extensible-enum defeats the purpose of it – it's not extensible anymore.
An OpenAPI (and JSON schema) enum means that the provider guarantees there won't be any values which are not listed. This means a consumer can rely on it, and e.g. map it to a Java enum class.
If we then get a different value, this mapping to an enum value will break – with e.g. an IllegalArgumentException on converting.
So extending an enum is an incompatible change. If an API provider wants to avoid breaking their clients, they need to align the change with them, giving them a chance to extend their enums (and code using it) before starting to actually send such values.
The idea of x-extensible-enum was to avoid this breakage by indicating already in the schema "these are the values we have right now, but please be prepared for additional values being added without notice in the future".
Thus a consumer needs to have a fallback behavior for values other than the known ones, so it doesn't break.
If you chose to map it to a strongly-typed thing like a Java enum, you also need some specific handling for when what you have doesn't match the known values (e.g. fall back to a default value, or to null or use some kind of union type of the enum and a string). This is not trivial to do in a generic way, so generally generators for strongly typed languages don't interpret x-extensible-enum, and just treat it as a normal string.
For a consumer, the interpretation would thus be similar to the later added examples from JSON schema.
(I'm one of the original authors of the specification of x-extensible-enum for Zalando's API guidelines. The current rule is in SHOULD use open-ended list of values (x-extensible-enum) for enumeration types [112], though we currently think about deprecating it.)