A Dyson swarm will keep you safe from any threat smaller than another Dyson swarm — and while you may not be able to "pack it up", you can use one to run to other galaxies… in fact, almost all of them… at close enough to the same time that light cones matter… and get the settlers moving at a significant fraction of the speed of light… and have a lot of redundancy.
If the point of a Dyson sphere is to collect energy, wouldn't it be enough to just use it or store it?
A stellar mass black hole might be an interesting "cold end" in this regard… if you can find or make one, but to do that you'd need to start with a Dyson swarm.
I don't think these semantic games are productive. Thermodynamics says you can transform energy. "Collect" in this context means using energy in a way that allows you to retrieve it in the future. For example, charging a battery or condenser with light with a PV panel, powering a motor that accelerates a flywheel, coiling a spring, heating a material, etc.
If this kind of thing appeals to a group with meaningful control over a Dyson swarm, given that Dyson swarms and the capacity to make them can also be used to build and power a rapid, direct, and near-simultaneous colonisation of all galaxies in our future particle horizon (with significant levels of redundancy, though obviously we can't determine if "significant" is "sufficient"), you should anticipate the first such group turning almost every star in the universe into a red dwarf (or brown dwarf, for those they don't care to colonise just yet) in very short order.
I don't know if anyone's been looking for signatures of this specific thing; though I am told that "1 AU sphere of room-temperature metal" would be quite easy to spot, if you downsize the stars first then the size of the corresponding room-temperature sphere gets smaller, and I don't have a quantifiable number for "quite easy" nor any sense of scale for how much effort is going into such searches.
If you're K2 just take the star and solar system with you. Stellar engines can be used to move stars. https://en.wikipedia.org/wiki/Stellar_engine
Shkadov thruster:
> After a period of one million years this would yield an imparted speed of 20 m/s, with a displacement from the original position of 0.03 light-years. After one billion years, the speed would be 20 km/s and the displacement 34,000 light-years, a little over a third of the estimated width of the Milky Way galaxy.
Caplan thruster:
> Caplan estimates that the Bussard engine would use 10^12 kg of solar material per second to produce a maximum acceleration of 10^−9 m/s2, yielding a velocity of 200 km/s after 5 million years.
Svoronos Star Tug:
> The Svoronos Star Tug can, in principle (assuming perfect efficiency), accelerate the Sun to ~27% the speed of light (after burning enough of the Sun's mass to transition it to a brown dwarf).
[Citation Needed]