For my own projects, I like to keep client-side code separated from the server-side code. The static site (with compiled JavaScript) gets deployed to S3/CloudFront, while the Sinatra API is packaged as a Docker image and deployed to ECS (or any container service)[1]. This means that Sinatra is only handling the API requests, and all of the markup, JavaScript, and other assets are served from a CDN.
[1] For this to work, you'll likely need to set up CORS on the server side, but that's well-supported now and fairly simple to set up.
Liveview can't be reproduced in ruby, currently. It might be a possibility once Ractor are there, but even in that case Ruby doesn't have the performance optimizations of elixir templates (and given how liveview works, those are needed). It might never be possible, or it might be possible in many years.
As for static typing, there advantages and disadvantages to that, I wouldn't consider that a minus at all. A good engineering culture brings you in the same place with a dynamic or static typed language. Same goes for a bad engineering culture.
In hindsight, I can't blame Rails for the direction it took; JavaScript's path (the language itself, as well as the tools) has been extremely volatile in that time. Rails is opinionated, which is part of what makes it great, but to be more opinionated on JS in the past probably would have been detrimental to the Rails community. I've felt the pain in my own work: every 2 weeks, it feels like my webpack/react/babel/etc toolchain and codebase need to be refactored because what was recently best-practice is now considered "legacy" and unsupported. When you embrace a specific set of technologies, you take on a certain amount of risk that those technologies will be deprecated, unsupported, or unpopular tomorrow.
I believe (hope is probably the better word) the JS landscape is getting more mature and stable, and it makes sense that the recent versions of Rails have incorporated more of what has become "standard" JS tooling. I'll always love Ruby, and even if I don't use Rails at the moment, I appreciate what Rails is doing and I directly benefit from the contributions of the Rails community.
More recently, I've been trying to learn some Elixir (those Phoenix LiveView demos look amazing), but not sure I'm ready to jump in 100%. Looks like matestack is essentially doing something similar with Ruby, so I'll be interested to see where it goes.