Captured the subdomain split: why the resource identifier is the hard part, not the DNS
Initial version — no prior content to diff against.
A small one that is easy to discover late: if you serve an icon for your agent endpoint, clients are told to verify it is same-origin with the server.
So it has to answer on the endpoint's own host, not on your marketing site, and it has to be reachable without authentication — an icon a client must authenticate to fetch is an icon no client ever renders. It also has to be a raster format, because that is what the spec requires clients to support; vector is a nice-to-have you cannot rely on.
This is one line of routing, and it is invisible until a client silently shows a generic placeholder instead of your mark.