Have you got any professional over seeing the design for you?
while you are correct in saying a garage conversion to habitable space is exempt from planning, this assumes you have no other extensions carried out.
there are building regulations that you need to comply to.
is the garage a step down from the main house?
also, the structure of the garage will not be on par with the main house.
floor slab build up and insulation?
wall insulation?
structural issues on the existing wall?
roof insulation.
ventilation and air tightness.
assuming you have all,of the above sorted, then you need to tell nobody.
if you go to sell, you will be required to produce a certificate of compliance with the building regulations and a certificate of exemption from planning regulations. You don’t reclassify the house anywhere. If the value increases then technically it could effect the band of your LPT.