In page https://docs.harvesterhci.io/v1.0/upgrade/automatic/ , there are some warnings about shutting down the VMs while upgrading the Harvester. Does it mean that we really need to shut down all VMs on every host and keep them all down while upgrading Harvester (causing potential downtime in the environment)? Is it still the case for upgrading from 1.0.1 to a future version?

That's what the page highly recommends - shut down (and backup) all your VMs in your cluster. At the top it also indicates this isn't the long term plan "Note we are still working towards zero-downtime upgrade, due to some known issues please follow the steps below before you upgrade your Harvester cluster" which I interpret to also include running VMs (unless perhaps you have a single node setup - with multiple nodes I'd expect the upgrade process to migrate all running VMs off a node before upgrading the node)

Ah that's a bummer. We are planning to have some sort of production-ready environment with multiple nodes in the next months where we invite some of our teams to test and break things. For them, zero downtime upgrade is an absolute necessity, I guess we will wait for a future version where this is resolved before going live.

This seems to be planned in the future, but right now this blocks the "enterprise status" of Harvester.