dogslayeggs

Better than ballistic dead reckoning, yes. I'm not sure whether it is better or worse than star trackers plus inertial navigation units at that time scale (INUs drift over time and need to be recalibrated every so often to fix that drift, but I really don't know how accurate star trackers are for position since I only use them for attitude measurement).

Mars was mentioned because it was written by a journalist, not a scientist. If you read all the quotes from NASA and the Italian agency, they only mention the Moon. Mars is too far away for any use of Earth/Moon/Lagrange based PNT satellites.

For lunar applications, power isn't really the limiting factor. It is the one factor we weren't sure about before this mission, so we figured that out. Another factor is geometry, with the long distances to the moon but small distances between satellites. A final factor is antenna directions and gain patterns. GPS antennas are facing the Earth and directional to the Earth (though there is a VERY tiny omnidirectional on the rear). The main antennas shove most of their power to the Earth's surface and have a small amount that leaks to the sides away from Earth. This mission used those side lobes, but because of the distances involved you don't see very many side lobes out at the moon. Even at GEO, space based receivers are only seeing a small number of satellites at a time because the Earth blocks most of the signal.

If NASA wanted a real PNT solution on the moon, they would need to have dedicated satellites with moon facing antennas. Even better would be moon surface repeaters with large antennas.

Nothing to prevent it except money. The issue with PNT satellites around Mars is how many satellites would have to be sent (smaller planet and less accuracy needed, so maybe we could get away with 12 instead of 24), plus the ground command and control stations plus monitoring stations. The ground part is probably the most critical piece of why GPS is so accurate, and I'm not sure we could do that from Earth. Definitely couldn't do the monitoring from Earth.

We'd have to be able to build an accurate ephemeris table for the Mars satellites, have accurate clock updates, monitor the signals being transmitted to do updates, etc. While we could do the commanding and controlling from Earth, I don't know if we could do the things from Earth that make GPS accurate. So not only would we have to send 12 satellites to Mars, we'd have to build monitoring stations on Mars to do the ground portion. Technically doable, just not financially feasible when we have star trackers and other navigation systems that work well enough for now.

I work on GPS satellites and am on the team working to define the next generation of GPS satellites. The beacon idea you are talking about is a terrestrial augmentation system. We have that here on Earth already, and it's critical infrastructure. On the moon, you could add nodes that receive GPS time and are used as a navigation aid on the moon. I doubt we would spend the money to put a GPS satellite at a Lagrange point anytime soon, since the benefits would be minimal for a single satellite. There is a lot more military interest in cis-lunar missions, though, so there might be benefits later. Repeater nodes on the moon's surface might be worth it, if we start doing more missions there.

Lagrange points are also pretty far away (the closest one is 1 million miles away, while the moon is 238,000 miles away. Current GPS satellites barely have the power to send a usable signal to the moon. To get a usable signal from Lagrange distances, the power would have to be much much higher (power drops as a square of distance. There's also the issue of building a satellite that lasts long enough in that radiation environment to make it worth it, since launching a satellite that big that far away is expensive. And that still would only help on the way to Mars, since Mars is another 99 million more miles past that (extremely rough numbers, since the average is 140 million miles from Earth but closest is 34 million miles and I have no idea what the distances would be to L4/L5 points).

They were only able to receive signals from the bare minimum to achieve a solution (4 GPS and 1 Galileo). Their achieved accuracy was +/- 1.5km and +/- 2m/s. That is good enough in astronomic scales to get you to a planet, but it isn't going to help failed landings or autonomous landings.

I don't think there was any new tech involved, just a receiver put on a moon lander to see if it could detect signals. And this won't really do anything for Mars for two reasons: 1) the signal strength would be too small for any reasonable antenna to detect GPS L1/L5 at Mars distances, and 2) the distance would make the geometry be unusable to trilaterate a solution... think about a triangle where two lengths are 100 million miles and the third length is 100 miles. That is a completely worthless geometry for trilateration of a position solution. Even if we could somehow detect a GPS signal at Mars, best case is we get atomic clock time.