Then there is heat. Using an oxy acetylene torch to heat up the whole assembly in an attempt to loosen the threads might work. What could go wrong?

Is it that entire brass threaded bit? (Admittedly, I do not know sodastream anatomy.) Is the brass bit simply screwed in too tight?

If it just needs to be unscrewed, I would use a trick similar to removing header studs on an engine, but modified.

Find two nuts that are the same size thread, but completely round off the corners on one of the nuts. Screw on the unmodified nut half way. Screw on the modified nut as tight as you can against the first nut. Use a socket wrench to apply torque on the first nut and it should give you just enough friction to unscrew the whole thing.

Needle nose pliers might work too.

Look on the bright side. At least it’s some of the most expensive bottled CO2 you can get so you don’t want to be wasting that stuff on just any drink. It’s high quality CO2, not some of that fake CO2 that some other gas company would pedal you.