If you were to just lay 2 wires next to each other, the area of
contact would be very small, just the tangential area. Twisting the
wires together will increase the area but soldering will provide the
most.

If you lay two solid wires next to each other parallel and in contact you
have two cylindrical shapes whose contact point is a single line. In the
real world, given malleable materials pressed together the metal will
deform microscopically and the line becomes a tiny bit wider than just the
infinitessimally thin line of pure geometry. I don't think that twisting
the wires changes this. Now the two cylinders take on a spiral shape as
does the line of contact but it's still just a line. The twist provides
the pressure only. Solder properly applied (sufficient heat) is going to
vastly increase the conductive contact between the wires.

Properly done the direct copper to copper contact should still be there as
well as the good mechanical tightness from the twist. The solder would
only add conductivity as well as prevent the twist from loosening.

No one has suggested using wire nuts AND solder. Make a good twist
connection with a wire nut, carefully unscrew it without loosening the
twisted wires, apply solder with good heat and just enough to flow into the
twists and not enlarge the overall joint, then put the wirenut back on
(should still grip the same) and put on the usual precautionary electrical
tape over the wire nut. A joint like that should last the ages. I once
used this technique for a junction box that was going to become fairly
inaccessible. Wire nuts alone would have been fine but, at least to me,
this was added peace of mind.