If you start with any reasonable universe simulation model prior and sample it to get a prior probability distribution over habitable planets forming - you get lots and lots of them

You don't need anything so fancy to get this conclusion. Empirical data and very basic models suggest that there are a lot of planets.

You would need enormous evidence - like actually searching all of the galaxy - to overcome this prior.

This does not follow, since you don't what the probabilities of other aspects other than habitable planets arising are. Moreover, we have effectively searched far beyond just one galaxy: if civilizations are common then they aren't doing anythng at all to show that: there's no sighn of stellar lifting, building Dyson spheres, or anything else that looks unnatural. That's a serious problem. We live in a universe that apparently has a lot of life bearing planets and the evidence shows that there's very little large-scale civilization. So what should one conclude?

Biophilic universes can probably engineer space-time by creating artificial new universes

"Probably" This means what? Why is this even a located hypothesis? Why should a universe being likely to have lots life be a universe more likely to have more new universes?

effectively shaping the prior probability distribution over the entire multiverse. (even if the physics of this seem low probability, it amplifies itself from nothing)

This is assuming an extremely strong form of multiverse, not just one that has differences in the fundamental constants of physics (questionable itself) but ones where the laws of physics themselves can divege. I see no good reason to assume such. Moreover, if one considers anything like that to be likely, it makes the situation even worse, because it is another reason to expect to see lots of civilizations, which we don't.

And finally, the entire idea of the great filter is based on an extremely specific and low probability model of future evolution of superintelligent civilization - dyson spheres and other nonsense.

Calling something nonsense doesn't make it go away. And yes, any specific construction may or may not occur- but the idea that civilizations exist and are leaving massive amounts of energy to go completely to waste requires an explanation. One should be worried when one is labeling stellar engineering as "nonsense" while taking engineering new universes in a broad multiverse setting as given. One of these is much closer to the established laws of physics.

See my reply here. Basically entropy/temperature is computational stupidity, and advanced civilizations need to move into a low entropy environment (like the intergalactic medium), becoming cold dark matter.

This is at best confused. Yes, doing operations takes energy. But you'd still rather use the available energy to do computations. There's no point in wasting it. As for the idea that this somehow involves "cold dark matter"- you are claiming that they are doing their computations made out of what exactly? Hidden MACHOs?