The other way around is true: the cubic meter figure is actually the more professional one, after all, built-up volumes are also applied for the constructed space, and not just areas. The square meter figure is due to the laymen’s imagination and is therefore more popular.
For you, what matters is the habitable area; whether you have a 2.75 ceiling or 3.50 is initially irrelevant.
Whether you want to live in your basement is not only a question of equipment and insulation, but also of room height. Potatoes are fine with the minimum height, so that you can go into the storage cellar without banging your head. The extra half meter of height cannot be given for free, not even with surface-mounted light switches.
I always have the impression that the unit € per m³ is used in offers wherever comparability is intended to be made more difficult.
Comparability is clouded elsewhere entirely: when provider X calculates according to the residential area ordinance and provider Y according to DIN.