I don't think there's anything in the current lore of starsector which goes into any amount of detail about toxic worlds other than; they're unpleasant and people generally don't bother with them.
To change the toxic atmosphere you need to know 'how' a particular planet is toxic before you can do anything.
For our purposes that's impossible, so we'd have to abstract it.
Eg: Venus.
Venus is ~90 atmospheres worth of carbon dioxide. You need to get rid of that gas somehow, there's two paths you can follow.
1. Physical.
Scoop up the gas however and dump it somewhere else.
Fling stuff at the planet and let the mass ejections jet parts of the atmosphere into space.
Install a solar shade to reduce the amount of radiation recieved by the planet, which will (eventually) condense the atmosphere and freeze the CO2 into dry ice.
Could also be achieved by floating large reflective surfaces high in the atmosphere.
2. Chemical.
Introduce large quantities of hydrogen to the atmosphere, the resulting reaction would produce carbon (probably as graphite) and water, which could be used to further the terraforming process.
Introduce large quantities of calcium & magnesium to the atmosphere, the resulting reaction would produce calcium & magnesium carbonates. This is a more effective carbon 'sink' than using hydrogen, but does not produce any water.
Posibly all these, with the exception of the 'mass ejections' would be useable as an abstracted means to accomplish this.
Scooping -> Atmospheric Siphon
Shade -> Already exists
Floating ->Atmospheric Reflectors
Chemical -> Atmospheric Condenser
The only thing to be wary of with the last one is that by 'large quantities' we're talking somewhere in the region of 1020kg. That's a lot of mass.
So it might be an idea if there's some manner of industry that will accomplish this that it would require a nanoforge to work at all in human timescales. The quality of which would dictate how fast it works.