It seems to work now. I have added this WMS:
wms:https://194.25.109.22/cgi-bin/mapserv?map=/usr/local/apache2/wms/biblio-lwl.map&FORMAT=image/jpeg&VERSION=1.1.1&SERVICE=WMS&REQUEST=GetMap&Layers=Bibliotheken&STYLES=&SRS={proj}&WIDTH={width}&HEIGHT={height}&BBOX={bbox}
And its tiles are correctly loaded:
Grabbing WMS https://194.25.109.22/cgi-bin/mapserv?map=/usr/local/apache2/wms/biblio-lwl.map&FORMAT=image/jpeg&VERSION=1.1.1&SERVICE=WMS&REQUEST=GetMap&Layers=Bibliotheken&STYLES=&SRS=EPSG:4326&WIDTH=500&HEIGHT=500&BBOX=11.1940135,53.4307610,11.1974347,53.4327993