It depends on what you mean by transmit information. It is possible for one party to read a true random number generator (the state of the photon) and transmit that reading faster than the speed of light to another party (the receiver of the entangled pair photon).

The physicist won’t call this transmitting information, but the information scientist has no qualms about acting on random data. And once you give data meaning, it is information. Maybe both parties pre-agree that N zero bits in a row from the digitized reading of the entangled photons is a start signal, and the bits that follow are used to make choices in whatever action is carried out. Now the first party has “sent” an instantaneous message informing of their actions.

To be clear I don’t think there is a clever gotcha here. But it is helpful in constraining what is meant by information locality here.

Your scheme sounds pretty similar to something like "if I find the house key in my pocket, I instantaneously know that my wife doesn't have it".

That's fine and useful for some things, but as you say it's not fundamentally quantum and it's not what's exciting about this development imo.

What is exciting about this development then? Because afaict this is the same thing.

There are several exciting applications that rely on a source of entangled particles. Super dense coding and quantum teleportation to name a couple. This is a step towards achieving those.