Even lowly mechanical disc brakes should work.
OP said near beginning about doubt if v brake levers are fitted. Are they? V brakes have more cable pull . The symptoms indicate they are not.
Have the callipers been usedx with the same levers before?
Clrearance between pad and disc is typically 0.5 mm or a bit less, at small distance the disc may rub at some point if slightly warped but can be gently bent back to shape.
If op had 1 mm clearance each side i.e. 2 mm, that is too much.
Lever should move about 1/5 of full travel before pads touch disc.
OP said near beginning about doubt if v brake levers are fitted. Are they? V brakes have more cable pull . The symptoms indicate they are not.
Have the callipers been usedx with the same levers before?
Clrearance between pad and disc is typically 0.5 mm or a bit less, at small distance the disc may rub at some point if slightly warped but can be gently bent back to shape.
If op had 1 mm clearance each side i.e. 2 mm, that is too much.
Lever should move about 1/5 of full travel before pads touch disc.