feat(companion): 60s mesh probe window + session pre-warm from the VPN service

Implements the app-side recommendations from the node diagnosis
(HANDOFF-2026-07-23): first session through the public tree takes 15s+
when it works at all, far beyond the old ~8s probe window.

- connect(): mesh ULA probed inside a 60s budget, 15s per-phase timeouts.
- ArchyVpnService: session warmer probes every saved node ULA as soon as
  the tunnel is up (5s cadence first minute, then 60s keep-warm) so the
  UI hits a warm session and it never idles out.
- Served APK: 0.5.5 (vc25); handoff updated with 25-ping evidence that
  public-tree discovery currently fails outright (supports the
  private-tree infra decision).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

docs/HANDOFF-2026-07-23-companion-apk-deploy.md

@@ -126,3 +126,19 @@ Chain of findings, each verified live:
   broader public mesh.
 - **Upstream:** report the direct-peer session-path asymmetry to
   jmcorgan/fips (0.4.1).
+
+## App-side recommendations implemented (23:30–23:50, Mac agent — 0.5.5/vc25)
+
+- Connect probe: mesh ULA now probed inside a **60s budget** with 15s
+  per-phase timeouts (rides out TCP retransmit backoff), replacing the old
+  ~8s window.
+- **Session pre-warm**: the VPN service starts probing every saved node ULA
+  the moment the tunnel is up (5s cadence for the first minute, then a 60s
+  keep-warm tick) — discovery/handshake cost is paid in the background, and
+  the session never idles out while the mesh is connected.
+- Extra evidence for the infra decision: from the phone on 5G, a 25-packet
+  ping burst to the node's ULA (25s continuous traffic, post-nginx-fix)
+  still got **zero replies** — discovery through the public tree isn't just
+  slow, it's failing outright. The private-tree option (detach fleet from
+  the public v0l mesh, root at vps2) looks like the real fix; app-side
+  patience only helps once discovery succeeds at all.