I have created the quick action for change the status and drop on it on the community ,through my "Community Plus" members case status is changing but not through "Community User"
The Customer Community Plus license is similar to the legacy Customer Portal: Enterprise Administration license.
So, Community plus license user will be able to update
Case even if its not shared with him (because they can act as delegated administrator).
On other hand, community license user needs the case to be shared with them to be able to update
Case. Check if user has edit access to Case using below query in anonymous window:
System.debug([SELECT RecordId, HasEditAccess FROM UserRecordAccess WHERE UserId = '--user_id--' AND RecordId = '--case_id--']);