TCP keepalive was configured (SetKeepAlivePeriod) but never actually
enabled (SO_KEEPALIVE) on accepted client connections. Go 1.26's
SetKeepAlivePeriod only sets TCP_KEEPIDLE — it does not call
setsockopt(SO_KEEPALIVE, 1). Without SO_KEEPALIVE the kernel never
sends probe packets, so dead connections from sleeping mobile clients
linger until the idle timeout fires.

Replace SetKeepAlive + SetKeepAlivePeriod with net.KeepAliveConfig
(available since Go 1.24) for explicit per-socket control:

  Idle:     30s   (time before first probe)
  Interval: 10s   (between probes)
  Count:    3     (failed probes to declare dead)

This detects dead connections in ~60s instead of relying on system
defaults (tcp_keepalive_intvl=75s, probes=9 → up to 11 minutes).

Increase the default idle timeout from 1 minute to 5 minutes.
MTProto clients send ping_delay_disconnect every ~60s, which resets
the idle timer. The previous 1-minute default created a race: if a
ping arrived even 1–2 seconds late the relay was killed. A 5-minute
window also survives typical mobile sleep periods (phone idle 2–5 min)
where the NAT mapping is still alive and the connection can resume
without reconnection.

Cherry-picked from 9seconds/mtg@5f81ae3 with fork-specific fixes:
- keep "time" import in run_proxy.go (used by throttle feature)
- fix network/sockopts_test.go import path to dolonet/mtg-multi