Is it possible to update Outcome Type on a Document via v3 REST API?

Yes, it is possible. See: Jive REST API v3.14 → Outcome entity

If you know the content id, you make the POST request to the url: https://mycommunity.com/api/core/v3/contents/123456/outcomes

The JSON payload is a simple object of:

{
  "outcomeType" : {"id" : 2}
}

Where the id is mapped to a specific OutcomeType. There should be a lookup table somewhere. Note: not all OutcomeTypess will work. I recommend checking via the endpoint:https://mycommunity.com/api/core/v3/contents/123456/outcomeTypes  . Some example are:

OFFICIAL("8"),

PENDING("3"),

SUCCESS("6"),

FINALIZED("2"),

WIP("9"),

OUTDATED("7");

If you are looking at a content object either by https://mycommunity.com/docs/DOC-123456/api/v3 or https://mycommunity.com/api/core/v3/contents/123456 , the resources object will have the /outcomes URL in it.