I have been very active in the PaaS in your cloud model in past. My analysis leads to the fact that no one has really pulled off heroku in your cloud kind product in recent time. There has been big exits like pivotal et al. Mind you it was before the kubernetes era. Post kubernetes era PaaS in your cloud has become very commoditized. As a PaaS-in-your-cloud (piyc) model as product you are not only competing with other product in the category list here [1] but also the internal platform teams in bigger orgs. Also, it is one of the competitive segment in devtool, devops space. Also having spent over 2 year in the space, I think heroku on AWS is an anti-thesis. I wanted heroku like experience I would start with heroku and not AWS. What you dont know yet is that it is a leaky abstraction as you start acquiring customers and very slow onboarding experience. AWS also made an attempt to build a heroku like product called app runner, which is I think is not that successful.
Similarly to serverless framework, it works on the developer's machine (or on a CI/CD server). You don't have to "install it to your account".
Compared to those "PaaS in your cloud" tools, you don't lose control, flexibility or security. You have the the full power and control of AWS (and other 3rd party providers Stacktape supports).
Stacktape is also very transparent about what it does. You can extend it (using AWS CloudFormation) or modify the generated template.
It was immediately obvious to me it was a wrapper over AWS which abstracts the infra to a little higher level, simplifying the initial setup and maintenance.
[1]https://github.com/debarshibasak/awesome-paas