Nero, you say you can't change the "server.servlet.context-path" value. I bet you say this because you don't want to break the API, but I think you can manage to change this without breaking the API. Set the context-path to blank, which is permitted. Then in your application change the "api" mapping, which I assume is currently "/", to "api".
Change server.servlet.context-path:/api to server.servlet.context-path:/ or maybe server.servlet.context-path: (no slash). (Supposedly this is the default so you might just remove this entry altogether.)
Somewhere in your application change @RequestMapping("/") to @RequestMapping("/api").
Now you can also have @GetMapping(value="/signout") and you will have resources at http://localhost:8080/logout and http://localhost:8080/api.
I don't know what mapping annotations you happen to be using, but hopefully this is clear enough.
http://localhost:8080/api/logout