Re: Serverless is essentially PaaS, basically shared-hosting
About AWS Lambda, I was quite underwhelmed by it's crude implementation. One has to re-upload a zip file with the complete source code, again and again. Even shared hosters that have support Perl and PHP since 1997 have been more advanced and offered FTP or upload form where one could re-upload only the altered source code files, not the whole repo everytime.
If you really want to, you can edit code in-situ, on the AWS console.
However, most people would rather keep their code in source control and use a framework to upload it, such as [serverless](https://serverless.com/). Just type "sls deploy" and let it assemble and upload the whole zip file for you, along with all the CloudFormation config to connect your app with any other AWS resources it needs.