What would be the optimal shape for the mixing container? Or would the difference be so small that it doesn't really matter?

My own thoughts are that the container should be a bottle with a long enough neck if you are pipetting the solvent directly from the container like I do. The neck isn't needed if you pour the whole thing through a separation funnel. You should choose the volume of the extraction so that the NPS-phase starts where the narrow part of the bottle starts. The narrow part should be large enough to fit the required volume of NPS. That way the small amount of NPS right above the base solution that you aren't able to get out without getting some of the brown mess is tiny compared to the whole column of NPS in the neck.

The bottle should be kept sideways during the waiting periods of pulls so that there is as large contact area between the two liquids as possible. Ideally the bottle should be flat like a hot water bottle to further increase the contact area.

The neck is to make pipetting easier and to be able to get as big percentage of NPS out as possible. The neck shouldn't be too narrow because that would make it hard to get the plant material in. This part seems indisputable for me but about the flatness of the bottle I'm not sure. The bigger surface area between the two liquids might only help marginally.

What do you guys think?

1L Erlenmeyer flask with a rubber stopper is what I use. If you don't have one handy a 1L glass juice bottle and lid works well also.

I used the same thick walled rum bottle with a wood topped cork stopper for several years, which was perfect for Cyb’s salt tek. The cork never showed any signs of damage and always sealed nicely. I finally threw it out after leaving a desmanthus soup in it for over a year. I think it matched your description just about perfectly with the exception of it not being flat. I always topped my basic soup up to the shoulder of the bottle and didn’t bother measuring my naphtha, I just filled the neck and kept doing pulls until I didn’t get anything.

The flatter bottle sounds like it might be a good idea for increasing surface contact between the phases, as long as you kept the bottle in some sort of spill containment. Though, I think you’ll get a little more mileage in that regard during the agitation process.