Direct Question
To answer your direct question: No. There are many cloud storage services, they are all different.
If you need rsync then suggest you rent a server to rsync your files to. If you want them backed up to the cloud you can use the AWS CLI and "aws s3 sync" on a cron job.
Implied Question
The wider question is difficult to answer because this is more a criticism than a actual question. If the question was "how do I back up my on-premise Linux server to AWS" I'd say
"Use the aws s3 sync command along with an s3 bucket with version control and encryption enabled", or
"use software such as restic or MSP360 to backup to AWS S3, B2, Google Cloud, etc". But that's not what you asked.
S3 Background
S3 is generic storage with its own API, and many other features such as versioning, encryption, etc. I imagine it was designed generic to make it easily usable by many operating system, devices, or anything else that needs it.
S3 has both an API and a command line tool, making it fairly easy to use.
Whether you call something an object or a file is largely irrelevant. S3 can be viewed as a file system by any OS, and you can even use tools like s3fs to make S3 look like a file system. That's not really what it's designed for, but it can do it. If S3 doesn't suit your use case, don't use it.
S3 General
AWS has multiple storage solutions. EC2 with EBS or EFS volumes is more likely suitable for your needs.