Short Update:
While the client side is still the same (I still use GPSLogger there), I changed my server side to the NextCloud app GPXPod in the meantime, which works really well for me.
(My GPSLogger was already saving the files onto my NextCloud so it was only logical to also use an NextCloud app for displaying them.)
p.S.: If somebody is wondering: yes, the blue track in the water is correct. It was quite the rough weather and our ferry couldn’t land for some hours …