IMO you will need to talk to your architecct too but I think there is nothing wrong with a space that is deep enogh to be able to access and then making sure that space is well insulated for sure . I would do the 4’ one at least then you can get in there if need be. That space will need to be sone just like your regular basement as far as insulation is concerned .Where I live there is little difference in cost to go deeper but that I think is very regional.

Hello! We did exactly this 1.5yrs ago in Buffalo, New York area, and contemplated pros-and-cons of a full basement extension, concrete footings, etc.

Our contractor proposed three concrete footings as well for a 12'x14' extension to a tiny bedroom (to convert it to a master bedroom with the tiny bedroom becoming the closet and bathroom). Instead of concrete footings, we went with 3 diamond pier 36" footings- our local code allowed it and we saved about 6K by not doing concrete. We have about 1' crawlspace underneath (did not extend the basement) and used a soffit system externally for ventilation. Our contractor did a good job with the insulating the floor (vapor barrier, sufficient thickness insulation, subfloor, hardwood floor, etc) Our contractor really came up with good solutions- all of the plumbing, electrical, HVAC etc. goes through the interior walls. A little more cost on this, but nowhere close to the cost of any of the other options. We've had this room over 2 winters and the floors are not colder than other parts of the house with a full finished basement below.

Good luck with your decision!

Consider a frost-protected shallow foundation or insulated slab.