You have to do it yourself. But it's not that hard. The easiest way of hosting multiple sites is probably to just assign multiple IPs to a single VM and simply run multiple servers simultaneously, each listening only on a single IP.

As far as the backup is concerned, Hetzner has the option of handling it for you for 20% extra money.

In my opinion this question seems like a good reason to get your feet wet just a bit. Just gaining some understanding of how things work under the hood is worth it even if you end up never using it professionally.

The basics of operating a (virtual) server to run your apps on could be seen as similar to learning the basics of cooking food. You can eat fairly well for the rest of your life without knowing a thing about it but if you just spend a single hour every week preparing your own food, you will become more familiar with the food itself. You would larn what individual flavors you prefer and where they come from, and you'll even be able to survive on less money if you would need to, or even survive more easily in a potential crisis where home delivery isn't an option.

If you spend an hour every week to learn some system administration (what people call "ops" nowadays) you'll be able to realize when you're being overcharged for simple services, feel the power of building a larger part of your stack yourself, play with new things, etc. Running multiple apps on a single host with proper backups is a trivial problem, especially if you know how to code, and in my opinion these things shouldn't be "left to the devops team" or seen as "IT stuff".

Not that long ago most developers had to know what environment their software ran in as part of their job, and despite many attempts to move away from it, this is still mostly true even if we have switched from the Linux CLI to cloud dashboards, CI/CD pipelines and Terraform scripts...