Any business that you can run from a home server 
    with a residential business line is not the kind 
    of business we are talking about here.

Depends on what you're trying to do.

You are not going to be able to run a Netflix competitor out of your garage.

You're not going to get high availability without some significant investment and even then you'll be at the mercy of whatever your ISP is doing upstream in the event of a power outage. I live in an area where we average something like 99.99% power uptime, but not everybody is so lucky.

You could, potentially, host something that serves up something non bandwidth-intensive to tens of thousands of users, give or take an order of magnitude. (SaaS, APIs, etc) You can do a lot of interesting things with a homelab and some of them are potentially profitable.

Perhaps more crucially: you're not exactly locked in to a homelab. You can start with that and once you reach a certain point, migrate to colo or cloud.

I have enough battery backup to run my rack for about 30 minutes, more if I shut down a node. That’s more than enough time for me to set up my generator and route power; it has an extended gas tank and can power the rack, fridges/freezers, fans, etc. for over 24 hours. I periodically run drills on this to ensure it’s doable, and that the gear works as expected.

If I’m not home, then yes, the latter would fail. Dual hardware failure is an unlikely scenario; single node failure is handled between K8s and Proxmox clustering.