I actually wasn’t aware that it could be run as a web service. I’d say do that.

So, I’ve done exactly this with gramps. I used a NUC running proxmox at my home.

I created a very simple https server with turnkey nginx running on the NUC proxmox instance. I host the gramps database exports there via a simple HTML page.

Tied it to a domain name and sent the link to my family, with instructions to install gramps and import the database.

EDIT: I used Let’s Encrypt for the SSL keys