Unable to register a Container Instance with ECS

I have a backend app that I have dockerized and want to run it on ECS using EC2 Launch Type , This backend app Is connected to RDS Instance In another account (i.e. backend app and RDS Instance are not In the same VPC) , So I have set up a VPC Peering Connection between them both. I have a few questions :

1- Does attaching an ALB with the Task to be launched In a Private Subnet is mandatory ? Taking Into consideration that the container launched In the task will connect to the RDS Instance In the peered VPC as If it Is In the same VPC through the peered Route, and the RDS Instance will respond back to the backend container through the peering connection route ? (I believe the NAT gateway will be used just to for the container In the task will be able to pull the docker Image from ECR) so, I don't get It where the ALB will fit in this current architecture ?

NOTE : I have already tried to connect ALB of IP Address type and connected it to the Task as a target group and I face the same problem where the task Is In Pending State .

2- After creating the Service , It Is Stuck in CREATE_IN_PROGRESS state , and I fixed It by following this answer as a guide https://repost.aws/questions/QUIz_pDFKUQ-222yiXF9wmww/ecs-service-creation-is-stuck-in-create-in-progress-status ,But after setting back the desired count to 1 , the task Is In a pending State forever , I followed this troubleshooting guide https://repost.aws/knowledge-center/ecs-tasks-stuck-pending-state , and after ssh into the ec2-Instance which Is supposed to host task and viewing the ecs.agent.log I can see this error

"Unable to register as a container instance with ECS" error="RequestError: send request failed\ncaused by: Post \"https://ecs.us-east-2.amazonaws.com/\": dial tcp 52.95.17.153:443: i/o timeout

Error registering container instance" error="RequestError: send request failed\ncaused by: Post \"https://ecs.us-east-2.amazonaws.com/\"

why would the ec2-Instance can't be registered with ECS ? , I have verified that the ecs-agent Is active using this command

sudo systemctl status ecs

This is my task definiton

{
    "family": "abc",
    "containerDefinitions": [
        {
            "name": "abc-container",
            "image": "<xyz>.dkr.ecr.us-east-2.amazonaws.com/my-backend:latest",
            "cpu": 1024,
            "memoryReservation": 1024,
            "portMappings": [
                {
                    "name": "abc",
                    "containerPort": 8080,
                    "hostPort": 8080,
                    "protocol": "tcp",
                    "appProtocol": "http"
                }
            ],
            "essential": true,
            "environment": [
                {
                    "name": "MYSQL_DATABASE",
                    "value": "value-1"
                },
                {
                    "name": "MYSQL_USERNAME",
                    "value": "value-2"
                },
                {
                    "name": "MYSQL_PASSWORD",
                    "value": "value-3"
                },
                {
                    "name": "MYSQL_PORT",
                    "value": "value-3"
                },
                {
                    "name": "MYSQL_HOST",
                    "value": "value-4"
                }
            ],
            "environmentFiles": [],
            "mountPoints": [],
            "volumesFrom": [],
            "ulimits": [],
            "logConfiguration": {
                "logDriver": "awslogs",
                "options": {
                    "awslogs-create-group": "true",
                    "awslogs-group": "/ecs/my-backend",
                    "awslogs-region": "us-east-2",
                    "awslogs-stream-prefix": "ecs"
                },
                "secretOptions": []
            },
            "systemControls": []
        }
    ],
    "taskRoleArn": "arn:aws:iam::<xyz>:role/ecsTaskExecutionRole",
    "executionRoleArn": "arn:aws:iam::<xyz>:role/ecsTaskExecutionRole",
    "networkMode": "awsvpc",
    "requiresCompatibilities": [
        "EC2"
    ],
    "cpu": "1024",
    "memory": "3072",
    "runtimePlatform": {
        "cpuArchitecture": "ARM64",
        "operatingSystemFamily": "LINUX"
    }
}

This Is my Dockerfile

FROM maven:3.9.6-eclipse-temurin-8 AS build
# Set Working Directoryc
WORKDIR /app
# Copy the pom.xml and the project files to the container
COPY pom.xml .
COPY src ./src
# Build the application using maven
RUN mvn clean package -DskipTests

#Use an Official eclipse-temurin image as the base Image
FROM --platform=linux/arm64 eclipse-temurin:8-jre
#set the working directory inside the container
WORKDIR /app
EXPOSE 8080
#Copy the built JAR file from the previous stage to the container
COPY --from=build /app/target/my-app.jar .
#set the command to run the application
CMD ["java","-jar","my-app.jar"]

This is my Docker Compose File where I reference the env variables defined in the task

version: '3.7'
services:
   my-app:
    container_name: my-app
    build:
       context: .
       dockerfile: Dockerfile
    ports:
      - "8080:8080"
    environment:
      - MYSQL_HOST=${MYSQL_HOST}
      - MYSQL_USERNAME=${MYSQL_USERNAME}
      - MYSQL_PASSWORD=${MYSQL_PASSWORD}
      - MYSQL_DATABASE=${MYSQL_DATABASE}
      - MYSQL_PORT=${MYSQL_PORT}

Parameters I used to create the Cluster :

• AWS EC2 Instances Selected

• AWS Fargate Unselected

• Created new ASG

• AMI : Amazon linux 2 (kernel 5.10)

• Desired Capacity: min 0 , max: 1

• SSH pem key enabled

• Instance type : t3.medium (2 vCPU, 4 GB Memory)

• Network :

     - VPC ( chose the VPC Which is Peered with the VPC which has the RDS Instance )
  
     - Subnet ( Only chose the Private Subnet with a NAT Gateway and a route to the peered VPC)
  
     - Security Group ( allowing All TCP Inbound Connections on all Ports)