those rheem heat pump units are damn nice, they take ambient air as heat source and are insanely efficient .. the down sides are they require 4 square feet of foot print, and they need tons of air flow to operate correctly .. meaning you cant just jam it in a tiny closet and forget about it .. and as awesome as it is, most folk wouldn't say it checked the right boxes as an architectural feature
i'm assuming you don't have existing radiant to tie into, or the build doesn't have provision to run piping out to the extension ?? i hate to say it, but this is one of the few times an electric wall hung boiler would make sense .. steibel eltron is the go to name for me, they have been doing this stuff in europe for a long time;
http://www.stiebel-eltron-usa.com/radiant.html
just make sure it is a boiler and not an on demand water heater .. unless it says 'suitable for space heating' on it it is simply not heavy duty enough for the rigors of extended operation