Yes, you need your cert to have both beansincup.se and www.beansincup.se
I don't know how you do that in EasyEngine. It looks like it should be setup by EE per their docs here. Maybe ask them if not sure.
One thing that may have prevented it from working is failure connecting to http://beansincup.se. That should be working before an HTTP challenge will work
curl -I beansincup.se
HTTP/1.1 503 Service Temporarily Unavailable
Server: nginx
Date: Wed, 23 Mar 2022 14:01:50 GMT
Content-Type: text/html
Content-Length: 206
Connection: keep-alive