[border-routing] always respond to Router Solicit with Router Advertisement (#7247)

This commit fixes the bug that BR may not respond to a Router Solicit
with a Router Advertisement when the BR itself is Router Soliciting.

This bug may cause Vicarious Router Solicitation more likely to fail
because BRs may failed to send RA for vicarious RS.

src/core/border_router/routing_manager.cpp

@@ -956,7 +956,6 @@ void RoutingManager::HandleRouterSolicit(const Ip6::Address &aSrcAddress,
     OT_UNUSED_VARIABLE(aBuffer);
     OT_UNUSED_VARIABLE(aBufferLength);
 
-    VerifyOrExit(!IsRouterSolicitationInProgress());
     otLogInfoBr("Received Router Solicitation from %s on interface %u", aSrcAddress.ToString().AsCString(),
                 mInfraIfIndex);
 
@@ -971,10 +970,7 @@ void RoutingManager::HandleRouterSolicit(const Ip6::Address &aSrcAddress,
     // Schedule Router Advertisements with random delay.
     randomDelay = Random::NonCrypto::GetUint32InRange(0, kMaxRaDelayTime);
     otLogInfoBr("Router Advertisement scheduled in %u milliseconds", randomDelay);
-    mRouterAdvertisementTimer.Start(randomDelay);
-
-exit:
-    return;
+    mRouterAdvertisementTimer.FireAtIfEarlier(TimerMilli::GetNow() + randomDelay);
 }
 
 uint32_t RoutingManager::ExternalPrefix::GetPrefixExpireDelay(uint32_t aValidLifetime)