Not that I would ever want to subject myself to shared hosting again, but I'm pretty sure you can run composer on your local machine to install the dependencies and then copy everything over, right? You've got to pay attention to what PHP modules are or aren't available on your shared host, but usually that's not too big of a problem.
I've started doing my composer installs offline when I foolishly tried to deploy a decently sized PHP project to a VPS with "only" 2GiB of RAM. For some obscure reason Composer eats RAM like it's cake and I couldn't get it to complete fast enough on the server itself.
Composer on shared hosts is a challenge, mostly involving retrying until it works. That's why I fetch most dependencies locally. Sometimes I mess with the dependencies a bit when a specific dependency requires information about how the operating system is configured, but most of the time that's not necessary.
It's PHP, but requires composer so not as easy to setup in shared hosting as old forum software like MyBB et al.