Tray reports Coder Connect as healthy while tunnel/DNS is broken; stale NRPT rule causes downstream tooling to hang or fail

Summary

The Coder Desktop tray indicator currently reflects "service running / signed in"
rather than "tunnel + DNS are actually serving traffic." When the dataplane goes
unhealthy (network flap, sleep/wake, control-plane DNS hiccup, etc.) but the
service is still running, the tray stays green while:

• The .coder NRPT rule and Wintun adapter remain in place.
• The embedded DNS server either keeps answering with fd60:627a:a42b::/48
  addresses that no longer route, or silently returns empty answers.

This misleads both users and downstream tooling that relies on *.coder
resolving correctly, producing two distinct user-visible failure modes.

Failure mode 1 — stale DNS still answering

Embedded DNS continues to return fd60::/48 addresses for <workspace>.coder,
but packets to those addresses go nowhere. Downstream effects:

• ssh coder.<workspace> (via a coder config-ssh-style ProxyCommand) hits
  coder ssh --stdio, which calls workspacesdk.ExistsViaCoderConnect,
  sees a fd60::/48 answer, commits to the direct-Connect path, and times out
  with dial tcp [fd60:...]:22: connect: operation timed out.
• coder ssh <workspace> (no --stdio) still works because it bypasses the
  Connect probe and builds its own tailnet client.
• Reported recovery in the field has been "reboot the laptop," which tears down
  the stale state.

(Filed separately against coder/coder as coder/coder#26669 for the CLI-side
defensive fix.)

Failure mode 2 — embedded DNS returns empty answers

Conversely, the embedded DNS server stops returning anything for <workspace>.coder
while the tray still shows connected:

> Resolve-DnsName -Name myworkspace.coder -Server fd60:627a:a42b::53
(empty answer — no IPAddress, no NXDOMAIN)

Downstream effects:

• File sync's remote directory picker (POST /api/v0/list-directory against
  http://<workspace>.coder:4/) fails with a raw
  System.Net.Sockets.SocketException (11001): No such host is known.
  surfaced to the user as a wall of stack trace in the directory picker dialog.
• Mutagen sync daemon repeatedly fails to resolve <workspace>.coder hostnames.
• Tailnet logs show failed to dial tailnet v2+ API, no matching peer, etc.

This is the same underlying state-management gap as coder/coder-desktop-windows#170, and tends to follow
the "service restarted without full off/on toggle" path from #149.

What I'd like to see

1. Tray indicator should reflect dataplane health, not just service state.
   When the tunnel cannot carry traffic (no peers, can't dial coordinator, embedded
   DNS not serving), the tray should turn yellow/red and surface a one-click
   recovery action ("Restart Coder Connect").
2. State should be coherent on tunnel-unhealthy. If the tunnel is not
   actually serving traffic, the NRPT rule and embedded DNS should either be
   torn down (so callers get a clean NXDOMAIN) or kept in lockstep with the
   tunnel's real status. The current "DNS lingers, tunnel is gone" intermediate
   state is what trips both failure modes above.
3. Friendlier error in the directory picker. Even after the underlying
   issue is fixed, list-directory should not surface a raw AggregateException
   stack to the user. Catch the socket / DNS failure class and render
   "Workspace unreachable — check Coder Connect status," ideally with a link to
   the tray.
4. Recovery shouldn't require a reboot. Today users in the field are
   resolving this by rebooting, or by toggling Coder Connect off/on (#149 notes
   that a service restart alone leaves the system in a broken state — the
   off/on toggle from the tray is the documented recovery path). Either the
   service-restart path should fully re-establish state, or the off/on toggle
   should be discoverable from inside the broken state (e.g. surfaced by item 1).

Reproduction

Hard to deterministically reproduce, but reported triggers include:

• Waking from sleep on a corporate machine (Zscaler / split-horizon DNS in the
  mix, per #149).
• Network flap while signed in.
• Control-plane DNS briefly failing to resolve, then recovering.
• Restarting the Coder Desktop Windows service while signed in (per coder/coder-desktop-windows#170:
  deletes the Wintun adapter, NRPT rule, and CoderVpnService entry without
  recreating them).

In all cases the tray UI continues to display the connected state.

Related

• coder/coder#26669 — companion CLI-side issue for ExistsViaCoderConnect to
  add a liveness probe so the CLI degrades gracefully even if Desktop is in
  this state.
• coder/coder-desktop-windows#170 — DNS publishing silently fails — workspace lookups return empty answers
  despite Connect being on.
• #149 — Not connected after waking from sleep.

Created on behalf of @mdanter