Very true, and most support systems are more than an email inbox. As far as we can tell, that's GOG's support system. I've been pointing out for a year or two now that GOG need to actually put in an ITIL compliant support app. If the user got a ticket number, and a way of escalating it, then there wouldn't be the need. However in GOG's case, this is exactly what the user needs to do (in fact, a forum post was required).

Yeah this has happened to me several times. If there is a 'next time,' you should preempt GOG support and contact Paypal, telling them that the purchase is void. Then contact GOG support so that they know about this. GOG support, as you have seen, is very prompt and will support any reimbursement request you make if your game never showed up on your shelf. They certainly did so when Paypal failed to let two of my purchases complete (aka paid money, no game.)

No, just contact GOG support. As you have seen, the situation is amicably resolved.