I try to dynammicly trigger my lambda by create rule , add lambda as target to that rule and add permission to the rule to invoke the lambda as follow:

const client = new CloudWatchEventsClient({
  region: region,
  credentials: { accessKeyId, secretAccessKey } 
});

//for simplicity i make constant variables here:
   const ruleName = "sendEmail-test-1"
   const cron= "(10 10 ? * * *)"
   const event = {foo:"boo"}

const putRule = async () => {
  const command = new PutRuleCommand({
    Name: ruleName,
    ScheduleExpression: cron,
    State: 'ENABLED',
    Description: Description
  });

  return await client.send(command);

putRule return metadaa with status code of 200 . also in the UI i can see the new rule.

Then I add target to this rule as follow:

const putTarget = async (ruleName: string, event: RuleObjectType['event']) => {
  const command = new PutTargetsCommand({
    Rule: ruleName,
    Targets: [
      {
        Id: ruleName,
        Arn: lambdaARN,
        Input: JSON.stringify(event)
      }
    ]
  });

  return await client.send(command);
  
};

Same here the status code in the response is 200 , and I can see in the UI that the rule has a new target which is my lambda.

But if I go the the lambda I dont see in triggers the new rule yet , so I add a permission to this rule inside the lambda as follow:

const addLambdaPermission = async (ruleName: string) => {
  const command = new AddPermissionCommand({
    Action: 'lambda:InvokeFunction',
    FunctionName: lambdaARN,
    Principal: 'events.amazonaws.com',
    SourceArn: `arn:aws:events:${region}:${IAM_ID}:rule/${ruleName}`,
    StatementId: `myProject-MyLambda-${ruleName}-permission` // Unique statement ID
  });

  return await client.send(command as any);
};

Again the response is with status code of 200 but still i dont see any changes
inside the lambda permission I dont see this new permission
inside lambda triggers i dont see the rule I just added.

What am I missing?