I agree that Moodle code should not be stored in EFS. I would just add that unless you are using a cluster of EC2 servers in an auto-scaling group you do not need to use EFS for Moodle data either. For smaller sites, it might be better to run a single EC2 instance and attach an EBS volume for data. Granted with this configuration you are not fully taking advantage of the flexibility, durability and scalability of the cloud. But for a small site, EFS might not really make sense.
Hardware and performance
Moodle + AWS EFS + filecachesd is it recommended?
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