[client] Apply lazy connection toggle to running engine

The daemon SetConfig only persisted the lazy connection flag to the
profile config; the running engine was untouched, so a UI/CLI change
took effect only after a down/up or daemon restart.

Wire SetConfig to push the change into the running engine via a new
ConnMgr.SetLocalLazyConn, which sets enabledLocally like an env/CLI
flag so a later management sync cannot override it, and starts or
stops the lazy manager in place.

client/internal/conn_mgr.go

@@ -107,6 +107,37 @@ func (e *ConnMgr) UpdatedRemoteFeatureFlag(ctx context.Context, enabled bool) er
 	}
 }
 
+// SetLocalLazyConn applies a local lazy connection override (UI / CLI / env).
+// While enabledLocally is true, UpdatedRemoteFeatureFlag (management sync) is a
+// no-op, so the local setting wins until it is turned off again.
+func (e *ConnMgr) SetLocalLazyConn(ctx context.Context, enabled bool) error {
+	e.enabledLocally = enabled
+
+	if enabled {
+		if e.lazyConnMgr != nil {
+			return nil
+		}
+
+		if e.rosenpassEnabled {
+			log.Warnf("rosenpass connection manager is enabled, lazy connection manager will not be started")
+			return nil
+		}
+
+		log.Infof("lazy connection manager is enabled locally")
+		e.initLazyManager(ctx)
+		e.statusRecorder.UpdateLazyConnection(true)
+		return e.addPeersToLazyConnManager()
+	}
+
+	if e.lazyConnMgr == nil {
+		return nil
+	}
+	log.Infof("lazy connection manager is disabled locally")
+	e.closeManager(ctx)
+	e.statusRecorder.UpdateLazyConnection(false)
+	return nil
+}
+
 // UpdateRouteHAMap updates the route HA mappings in the lazy connection manager
 func (e *ConnMgr) UpdateRouteHAMap(haMap route.HAMap) {
 	if !e.isStartedWithLazyMgr() {

client/internal/engine_lazyconn.go

@@ -0,0 +1,19 @@
+package internal
+
+import (
+	"errors"
+)
+
+// SetLazyConnEnabled applies a local lazy connection override to the running
+// engine. It pins the setting like an env/CLI flag, so a later management sync
+// cannot override it. syncMsgMux guards ConnMgr, which is not thread-safe.
+func (e *Engine) SetLazyConnEnabled(enabled bool) error {
+	e.syncMsgMux.Lock()
+	defer e.syncMsgMux.Unlock()
+
+	if e.connMgr == nil {
+		return errors.New("connection manager is not initialised")
+	}
+
+	return e.connMgr.SetLocalLazyConn(e.ctx, enabled)
+}