Both halves change: the parent, because a swarm runs one homeserver and
every hive reaches it; and the label, because `chat` names the service
people use rather than the protocol it speaks.
⚠️ `serverName` is deliberately NOT touched, and the two are now
documented as the different things they are. `gatewayHost` is a routing
detail -- the API listener nginx proxies `/_matrix/*` to, which clients
rediscover through `.well-known`. `serverName` is the matrix identifier
baked into every user and room id: changing it is a different
homeserver, not a rename, so it still falls back to the bare hive
domain. A note at the fallback says so, since that binding is where a
future edit would most plausibly "fix" the inconsistency.
Old deployments pin `matrix.<hive domain>` -- exactly what the old
default rendered -- and dnsmasq already lists `gatewayHost` explicitly,
so a pinned or moved name stays routed either way.
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