It depends. I’ve ran small websites and other services on a old laptop at home. It can be done. But you need to realize the risks that come with it. If the thing I’m running for fun goes down. someone might be slightly annoyed that the thing isn’t accessible all the time, but it doesn’t harm anyones business. And if someones livelihood is depending on the thing then the stakes are a lot higher and you need to take suitable precautions.
You could of course offload the whole hardware side to amazon/hetzner/microsoft/whoever and run your services on leased hardware which simplifies things a lot, but you still run into a problem where you need to meet more or less arbitary specs for an email server so that Microsoft or Google even accept what you’re sending, you need to have monitoring and staff available to keep things running all the time, plan for backups and other disaster recovery and so on. So it’s “a bit” more than just ‘apt install dovecot postfix apache2’ on a Debian box.
I have no idea about cozy.io, but just to offer another option, I’ve been running Seafile for years and it’s pretty solid piece of hardware. And while it does have other stuff than just file storage/sharing, it’s mostly about just files and nothing else. Android client isn’t the best one around, but gets the job done (background tasks at least on mine tend to freeze now and then), on desktop it just works.