The idea is that once the rock has been infected, there are thousands of years during its transit to fully affect any change necessary to spread spores our during a pass-through on the next system.
Getting those spores the delta-v needed to escape the interloper, and arrive on a planet, is going to be exactly as problematic as getting them to the interloper to start with - but instead of starting with the technological base of an entire planet of humans, you are trying to solve the problem with the technological base of a small cold rock with some ftozen tardigrades on it.
This seems like an even less tractible problem than the one we started with.
Well, that's the whole point: only life itself tends to have the kind of deployment package that could do it.
Not so. Life is shit at space travel. It took over three billion years to develop space travel, with an entire planetary surface - including a lot of water and a lot of atmosphere - to work with.
And our best efforts have resulted in non-life probes. Nothing on Voyager is alive. Likely nothing alive has made it past the Moon.
It also tends to produce the only viable deployment packages for containing a whole human organism worth of information in a package smaller than a grain of dust.
Not on tiny rocks in a hard vacuum, it doesn't.
I would expect that the majority of space is, as you say, quite cold and empty with few opportunities to collect energy.
I would expect that you don't grasp just how much of an understatement that is.
The majority of the
solar system is completely empty, and has only the Sun to
provide energy - and for the vast majority of the solar system, the Sun is a long way away, and provides three eighths of bugger all energy.
The overwhelming majority of
galactic space is far emptier, and has no nearby stars.
And the overwhelming majority of space lies
between galaxies, and is emptier still.
Assume that somehow an alien civilization, keen to seed life through the universe, had managed to get some bacteria, or even some tardigrade-like life onto a rock on an interstellar (or even intergalactic) trajectory - how, exactly, is that life getting off that rock? Survival is unlikely; Evolution is even less likely - there is no source of energy, other than for a few days every several million years, when the rock passes close to a star.
If it takes billions of years for life to evolve the ability to travel through space, when it is situated a comfortable 150 million km from a nice stable star, how long will it take if it is only in such an advantageous energy collecting position for a few billionths of a percent of the time?
By the time your "information package" has managed to solve this problem, there won't be any stars or planets left to travel to.
3I/ATLAS could be teeming with wonderfully engineered alien tardigroid life, fully loaded with the genetic information needed to turn any planet into an alien biosphere to rival that of their home planet. We would never know about it; And it could no more influence any of the planets in our Solar System as it pases through, than it could have had it passed by a couple of lightyears away.