I don't know too much about slim or rsync - but to me what it seems like you're asking about is deployment and how that would work in Laravel.
Well that's not really the issue Laravel is trying to solve I think. There are first-party tools like Laravel forge that give great options for deployment automation and work really well with version control tools github or bitbucket, and just 'publish' a particular commit. Forge has a lot of functionality built into their deploy scripts that you can customize, but frankly it's built for Laravel and composer and a particular toolset. If you're not using that you may run into some trouble and have to do some funky work arounds.
For example I have one project that is a pure react project with Vite and no backend, and I'm serving it over forge, but there was a bit of trouble getting it to work at first (though eventually it worked). It's just documentation, and there is a search feature that needs to be re-compiled when the files it searches over changes, the way it works is through a shell command, and I have that on the deploy script, I imagine a lot of that script could be added to that forge deploy script. (But it is a paid service)
As for 'cruft' that would have to be managed by composer rather than laravel, production dependencies kept separate from dev-depencies in the composer.json file. MySQL managed with migrations rather than just adding columns.