There is a VPC connector enabled Route all traffic through the VPC connector and a firewall rule to allow all egress traffic for the VPC. Still, I am not able to connect to the RabbitMQ instance(cloudamqp) due to timeout.
I realized that the issue is about using Cloud Run VPC accessor for all traffic without a NAT gateway. After creating a NAT gateway for the related VPC, the issue resolved.
Using the VPC accessor for only the internal traffic can also help in this case. But, if you need to use static IP to route outbound requests to external endpoints then you have to use Cloud Run + all traffic through VPC Accessor + NAT.