Interesting question. I did a bit of reading and gave it some thought and and I can sort of give an answer, though I invite corrections and input from anyone more knowledgeable than me.
First, those 2 galaxies are enormous. I didn't see specific sizes listed, but per this paper:
1.2-1.5 x 10^14 solar mass fossil group
That's about 100 Andromeda galaxies. Also, since what we're seeing is 4.6 billion years old, it's reasonable to assume that those 2 galaxies probably have more free dust and gas and, being larger, the gravitational collision is happening at higher speed.
That's really the question with how much background x-ray radiation you get when 2 galaxies collide. how much free gas and dust and how fast the galaxies move into each other. My guess is that being larger, and younger, those 2 galaxies are glowing much more brightly than the Milky-way and Andromeda will 4 billion years from now.
As to how intense the glow is, my hunch agrees with yours, it's probably not very bright if you're there. The faint glow and the 2 bright eyes you see in the picture are long exposures. This site (scroll to the bottom) says it's 19 hours and 30 minutes of exposure. Andromeda, for example is barely visible to the naked eye, but when photographed it's made many times brighter. I'm not smart enough to say for 100% sure, but my guess is that the faint purple glow would be barely visible, if visible at all, assuming it even reached into the visible spectrum, which X-ray's don't. Chandra might be setting the color to a visible spectrum in the picture.
How dangerous is it? Again, I'm guessing, but I think in the Milky-way-Andromeda collision, we'd probably get more UV from the sun than we would from high speed gas and dust collisions, but that's just a guess. It would be kind of fun if the entire night sky glowed a little bit though.
As far as the Milky-way-Andromeda collision, Wikipedia says that there won't be much free gas in the collision, here, so it's a safe bet there won't be any visible glow in the sky and not even that much of an acceleration of new star formation, though there should be some. The Milky-way currently forms about 7 new stars every year, and that I imagine will gradually slow down over the next 4 billion years, then speed up significantly as the collision gets underway, but from the point of view of Earth, I don't think there's any guarantee we'd get a close look at any new star formations.
Here's a fun article/interview on the collision between the Milky Way and Andromeda, though I think Roeland van der Marel might be exaggerating the new star formation a bit if we're to believe Wikipedia where it says there won't be much free gas.
As for the speed of our collision, Andromeda is currently heading towards us (or, we're heading towards it, whichever you prefer) at about 110 km/s source. and it's currently about 2.5 million light years away. Source.
Covering 2.5 million light years (about 24 million trillion km) in 4 billion years (126 million billion seconds), works out to an average speed of 190 km/s, so we can roughly estimate that the speed of impact between our two galaxies will reach a peak somewhere around 270 or so km/s. But (see video you also have to take into account the rotation speed and it appears (video above) the rotations will be going in opposite directions when the galaxies collide. We orbit the Milky way at about 250 km/s and Andromeda, being larger, probably a bit faster orbit speed. Adding the 2 velocities together, in our neck of the woods, we might see some relative velocity and some gas & dust collisions at (guessing here, cause I don't know if the rotations will slow down as the galaxies approach), but lets say 500 to 600 km/s or so. For any close bright stars from Andromeda, that could be fast enough for visible changes to a few near-by Andromeda stars in constellations over a single human lifetime.
Perhaps, we'll pass through an oort cloud of another star every few thousand years or so, perhaps even the occasional kuiper belt equivalent, every ten or 50 million years - er, maybe. We could see some very impressive meteor showers and perhaps an occasional, slightly more frequent, dinosaur killing level comet or meteor impact - but I'm just speculating. There might be lots of interesting things to see between 4 and 5 billion years from now.
When stars form they can be (per this website) 100 to 200 times brighter than they are during their main sequence, so if our solar-system finds itself nearish to a colliding gas cloud and some new star formation, that could be interesting. Likewise if we pass near the core of Andromeda we might, for a while, have a very bright night sky.
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