[bbr] fix primary BBR registration flakiness on leader (#12783)

This commit fixes an intermittent failure in the Nexus test
1_2_BBR_TC_2 by ensuring that the Backbone Router (BBR) service
is registered immediately when a node assumes the Leader role and
no primary BBR is active.

Previously, BbrLeader only tracked network data changes, and
BbrLocal applied a mandatory jitter delay before registration.
This created a race condition where another node could register
its BBR service before the new Leader, causing the Leader to
incorrectly skip its own registration.

Changes:
- Update BbrLeader to monitor role changes (kEventThreadRoleChanged).
- Modify BbrLocal to bypass registration jitter if the node is
  the Leader and there is no existing primary BBR.

src/core/backbone_router/bbr_leader.cpp

@@ -127,7 +127,7 @@ const char *Leader::DomainPrefixEventToString(DomainPrefixEvent aEvent)
 
 void Leader::HandleNotifierEvents(Events aEvents)
 {
-    if (aEvents.Contains(kEventThreadNetdataChanged))
+    if (aEvents.ContainsAny(kEventThreadNetdataChanged | kEventThreadRoleChanged))
     {
         UpdateBackboneRouterPrimary();
         UpdateDomainPrefixConfig();

src/core/backbone_router/bbr_local.cpp

@@ -246,15 +246,18 @@ void Local::HandleBackboneRouterPrimaryUpdate(Leader::State aState, const Config
     // Wait some jitter before trying to Register.
     if (aConfig.mServer16 == Mle::kInvalidRloc16)
     {
-        mRegistrationTimeout = 1;
-
-        if (!Get<Mle::Mle>().IsLeader())
+        if (Get<Mle::Mle>().IsLeader())
         {
-            mRegistrationTimeout +=
-                Random::NonCrypto::GetUint16InRange(0, static_cast<uint16_t>(mRegistrationJitter) + 1);
+            mRegistrationTimeout = 0;
+            Get<TimeTicker>().UnregisterReceiver(TimeTicker::kBbrLocal);
+            IgnoreError(AddService(kDecideBasedOnState));
+        }
+        else
+        {
+            mRegistrationTimeout =
+                1 + Random::NonCrypto::GetUint16InRange(0, static_cast<uint16_t>(mRegistrationJitter));
+            Get<TimeTicker>().RegisterReceiver(TimeTicker::kBbrLocal);
         }
-
-        Get<TimeTicker>().RegisterReceiver(TimeTicker::kBbrLocal);
     }
     else if (aConfig.mServer16 != Get<Mle::Mle>().GetRloc16())
     {