Lambda code does not get zipped during `package` command when using substacks - amazon-web-services

Question

I am using CloudFormation for creating lambda functions. The lambda functions are stored in a separate file and then recreated using aws cloudformation package command. This works fine and the stack gets deployed successfully:
# Filename: auth/auth.yml
# Lambda JS file: auth/lambda-pre-signup.js
Resources:
## Other resources here
MyPreSignupLambda:
Type: AWS::Lambda::Function
Properties:
Architectures:
- arm64
Code: 'lambda-pre-signup.js'
Handler: 'lambda-pre-signup.handler'
Runtime: nodejs16.x
PackageType: Zip
Role: !GetAtt MyRole.Arn
Command:
aws cloudformation package --template-file auth.yml --s3-bucket my-bucket --output-template-file generated-auth.yml
aws cloudformation deploy --template-file generated-auth.yml --stack-name test-stack --capabilities CAPABILITY_IAM
However, when I create a root stack template and reference lambda, I get an error:
Resource handler returned message: "Could not unzip uploaded file. Please check your file, then try to upload again. (Service: Lambda, Status Code: 400, Request ID: xxxxx)"
When I check the S3 bucket for the uploaded file, the source code is there but it is not zipped (I can download and directly view the code without needing to unzip it).
Here is my current CF template for root stack:
# Filename: root.yml
Resources:
MyAuth:
Type: AWS::CloudFormation::Stack
Properties:
TemplateURL: ./auth/auth.yml
Command:
aws cloudformation package --template-file root.yml --s3-bucket my-bucket --output-template-file generated-root.yml
aws cloudformation deploy --template-file generated-root.yml --stack-name test-root-stack --capabilities CAPABILITY_IAM
Is there some option in the package command to make sure that the uploaded lambda code is zipped?
EDIT: Wrote a wrong argument