The existing convention is just to convert diagrams to an image (svg or png). Granted, this has the obvious downside that it’s hard to update, but there’s some benefits: it doesn’t require any in-tree tooling, the rendering is completely predictable, and people can use their preferred tools.
The bot that generates the site should have a standard Linux install of both Sphinx and Graphviz; if that’s enough, it probably works? Probably worth writing a test commit before you do too much work in this direction.