I can't see what GOG can really do other than limp along behind the Steam version and just be happy to be around?
a) pressure Hello Games into providing a fix. Workarounds are known, so fixing this would be easy. But maybe, as you say, GOG hasn't the power to pressure Hello Games into doing anything.
I'm sure they have done this already, in that they have brought up the issue with Hello Games. I tried the zen-desk of Hello Games myself and did not even receive a reply.
b) they could stop selling the game until it is fixed - which would anger some customers.
They 'might' have already tried this, just going on the 'peak frostiness' between HG and GOG a few years back. If so i suspect HG were just like 'OK but refunds are on you as per the agreement of sale'. Conjecture.
c) they could get permission from Hello Games to fix it themselves. Again, a workaround is possible. GOG just has to apply it. Hello Games would have zero work with this.
This would be hard (legally) to do in the best of corporate relationships (IP and control of rights being what it is).
d) at the very least they could keep the last version of the game without the DRM available as offline backup installer. In that way everyone who wants it could download a 100% DRM-free version. But they don't. That is a decision that is entirely in their camp.
And at the very, very least they could communicate what is being done. The silent treatment of their customers just shows that there is nothing to tell. I.e. they have done nothing that they could communicate. Or the blues are even forbidden from talking about the issue. Same as in the case of Absolver. (in the case of that game GOG should classify it as pure multiplayer game like Gwent - or stop selling it)
The last point is legit. I had to push GOG support to provide me a link to the current version of NMS i am playing (Synthesis 2.27 iirc, the last patch of that update version), which is the version before the 'Living Ships update' that introduced the online requirement. GOG 'could' provide that in the 'offline installer section, clearly defined as what it was to not confuse it with the current version etc, and stating why it was there maybe to bring greater attention to the issue?
So last point aside (as that is something GOG could setup fairly easily) all the rest is on Hello Games. They won't (seemingly) respond to zen-desk requests for GOG customers, they introduced the online requirement for the single player game, they are in the best position to fix the issue (as it is their IP), but they don't seem to want to.