Do we have an example of a real quantum computer doing some kind of a computation that is not easily accessible by the regular computer?

I keep hearing about "the promise" and "achieving quantum supremacy" (again!), but is there a real example of a quantum machine doing something useful in real life?

No, there are none; the closest we currently have are various special purpose and more or less hard-coded machines that demonstrate that scaling exists; various general-purpose machines operating on handfuls of qubits demonstrating the various gates; and various snake oil scams that may or may not have semi-respectable research divisions associated with them.

https://www.newscientist.com/article/mg26735582-700-how-a-we...

The Venn diagram of "useful" and "not possible on a classical computer" has demonstrations on both disjoint ends but is currently empty in the intersection. For now. I fully sympathize with the hype-fatigue though.

No. It's as if there's a "No computing with this shit" theorem, enforced by nature alongside "No FTL communications," "No hidden variables," "No, you can't build a transporter, not yours," and "No cloning."