Hey, I’m new here so please be understanding 
I managed to configure everything. HA works locally and remotely.
Unfortunately, the connection only works via http.I have added the ISRG CPS v3.3 certificate to the domain and eg DSM reads this normally (opening https)
does anyone know how to do it also in HA?
Is HA in VM or Core?
For Core you need to copy certificate to configuration folder of HA and specify location (name) of it configuration.yaml file.
Other option, that I also use is don’t bother. Use internal Synology Reverse Proxy (in Configuration Panel - Application Portal) and make it so that traffice incoming to HTTPS port from outside, ends as HTTP traffic inside - pointing to IP address of Home Assistant, and port you are using.
This should work with Core version but also with HA in VM.