healthcheck: answer 503 when the last round of DNS checks reached no root server (closes #302)

The health check answered ok while every DNS lookup failed, as on a
network that intercepts DNS queries. A lookup whose root servers give no
usable reply now fails with ErrNoRootServerAnswered. At the end of each
round of DNS checks the watcher records whether every lookup failed with
it or with ErrIntercepted; the health check then gives status error, and
/.well-known/healthcheck and /health answer 503. Until the first round
finishes it stays ok.

The health check now depends on the watcher, so fx builds the watcher
first: its first round starts before the HTTP server listens, and the
server tests' fx graph includes it. NewWithRootServers lets tests start
a resolver's walks at real servers that are not root servers.

Model: opus-5-5

TODO.md

@@ -19,6 +19,9 @@ milestone: https://git.eeqj.de/sneak/dnswatcher/milestone/7
 
 # Completed Steps
 
+- 2026-10-18: the health check answers 503 with `status` `error` when no lookup
+  in the most recent round of DNS checks got a reply from a root server, as on a
+  network that intercepts DNS queries (closes #302).
 - 2026-10-16: the first reply marked "recursion available" from a root server's
   address, a refusal included, stops the lookup with "this network intercepts
   DNS queries", so on a network that sends DNS to a resolver dnswatcher and its