transgender people, whose gender identity differs from their biological sex, may be provided single rooms, where appropriate

You are not assigned male, you fall in the sex category male at birth. Sex is immutable and cannot be changed unlike gender, therefore in wards based on sex you will be put in a male ward. Unless as the article lays out you get your own room, which is the likely and most preferred outcome for all inpatients.

I was correcting a factual mistake, the conflation of sex and gender in this case, far from whining.

Incorrect, they are single sex wards not single gender wards. Females should be on a Female ward and Males on a Male ward which is correct if wards are decided based on sex and not gender.

If you are only accessing the services while connected to tailscale using the tailscale admin console you can add a nameserver, and then point that to a local DNS resolver. The local resolver can point the URL you want to the IP with the ports you want. I don’t know if Synology has DNS resolving apps but that might be an option, otherwise you could run pihole or something similar to achieve this.