How to organize Terraform modules for multiple environments?

Every Terraform guide on the web provides a partial solution that is almost always not the real picture. I get that not everyone has the same infrastructure needs, but what worries me is that the common scenario, including:

1. Multiple environments (e.g. dev, stage)
2. Remote backend (e.g. AWS S3)
3. Some basic resources (e.g. S3 buckets or EC2 instances)

isn't presented anywhere on a real example project. I'm looking for just that.

In the meantime, I have researched and concluded that apart from those needs, I also want:

1. To utilize modules.
2. To NOT use workspaces, but rather a distinct directory-per-environment approach.
3. To NOT use a terragrunt wrapper.

This is my current structure, which does not utilize modules - only a root module:

infra/ --------------- 'terraform init', 'terraform apply' inside here*  
     main.tf --------- Sets up AWS provider, backend, backend bucket, DynamoDB table   
     terraform.tfvars   
     variables.tf ---- Holds few variables such as aws_region, project_name...

I think my desired structure folder tree (for a simple dev & staging simulation of a single bucket resource) would look something like this:

infra/  
     dev/  
        s3/  
            modules.tf ------ References s3 module from local/remote folder with dev inputs   
     stage/  
        s3/  
            modules.tf ------ References s3 module from local/remote folder with stage inputs   

But what about the files from my previous root module? I still want to have a remote backend in the same way as before - just that now I want to have two state files (dev.tfstate and stage.tfstate) in the same backend bucket? What would the backend.tf files look like in each sub-directory, and where would they be? In s3/ folder or dev/ folder?

It's kind of confusing since I'm transitioning from a root module terraform init approach, to a specific sub-directory terraform init. It's not clear to me whether I should still have a root-module or another prerequisite folder (for example: global/), which I should init at the beginning of the project, and which is basically left alone from that point on (since it created the buckets which dev/ and staging/ reference).

One more question: if I have s3/, ec2/, and ecr/ sub-directories inside each environment, where do I execute the terraform plan command? Does it traverse all sub-directories?

When I have the answers and a clear picture of this above, it would be great to improve it by DRYing it up, but for now, I value a more practical solution through example rather than just a theoretic DRY explanation.