With this project falling behind, and the reducing likelihood of delays in the Lunar Gateway/Artemis program, I think there's a good chance that NASA and the ESA will not have access to a space station following the ISS's decommission. It's not the only "public-private" partnership for an ISS successor, but I don't think the other candidates are making much progress either.
I also thought that this quote was pretty amusing, and highlights the futility of trying to privately fund commercial station projects:
To bring in some much-needed cash, Axiom Space started selling seats for trips to the ISS on board SpaceX's Crew Dragon spacecraft.
It was also awarded a NASA contract to fund a space suit for the first crewed mission to the lunar surface, Artemis III.
But the suit appears to have been a massive distraction — not to mention a major money pit — from its plans to build a space station. SpaceX trips to the existing orbital outpost were also not a sustainable solution to Axiom Space's woes.
"Turns out that there's not a lot of billionaires that want to set aside their life for 18 months to go train to be an astronaut for the ISS," a former Axiom executive told Forbes.
That's pretty good. I just want them to just use their moon rover to push over the flag we did there. We wouldn't be able to set it back up.
That would be the longest rover trip ever by a factor of like several thousand.
Good, that would force us to watch knowing we can do nothing to prevent it. The suspence might even get congress to approve making a moon battle bot to send them to stop them.