Don’t think git as a sync storage, more like to merge works.

If you need to share files between computers use a shared storage.

Always use the right tool for the job. Mount a shared storage or use synctools rsync, etc

https://github.com/axllent/mailpit

In AWS, you can use Aurora to scale reads access over multiple instances. It’s easy to setup and you can use scaling policies to follow your load. You need to check your billing, it’s not the cheapest service.