Yes, you do need some kind of VPS, unless you want someone else to run it for you. (We could run it for you, if you wanted, but you'd be trusting us.)

The issue is that Shopify needs to "redirect" to another website to show the invoices... there's no way around that.

So you basically have to host some kind of website...

BTW.. you said "a simple compute worker" -- what do you mean by that?

If you're technical and want to suggest another way to do this, please do look at the github repo and tell us if you have any great ideas... but I think you will find that ultimately you have to run SOME kind of web server to show the invoices.... and it must be on a domain that you control, too. (Again, unless you wanted someone else to run BLFS for you.)