For almost every object in Lightning, a record specific Custom Action, when added to the page layout, appears as a button in the Highlights Panel. However, Cases (and Work Orders) are an exception. As stated in this H&T article: https://help.salesforce.com/articleView?id=actions_in_lex.htm&type=0
Actions on cases and work orders appear in a different way than on other records. On case and work order records, the page-level action menu contains custom buttons and supported standard buttons. Quick actions appear on the Chatter tab.
I get why this was done, but it's not always the desired behavior. In fact, it's buggy when using a Flow-based Action:
We need a way to choose if an Action appears in the publisher or as a button, perhaps within the Lightning App Builder (or on the Action itself).