Sorry, I know I'm uneducated on all of this. I've been reading and researching extensively but I've always though fireplaces and/or inserts were a lot less efficient than a stove. How much heat do get when the power goes out and you don't have the blower?
Pretty much the same depending on the efficiency of your installation. First, you have to distinguish the efficiency of your heating unit (stove/fireplace/insert) versus the efficiency of your installation. The efficiency given by the manufacturer states how much heat the unit distributes to its surrounding versus the amount that goes up the flue. For a modern wood burning unit that is in the 70% to 85% range under testing lab conditions. However, the efficiency of your installation determines how much of that heat will actually end up in your home. Put an 80% efficient wood stove in an unfinished basement with cement walls and slab floor and you will heat a lot of ground but not your home. Same for putting an insert into an old masonry fireplace made out of brick that sits on an exterior wall. The insert will heat the brick which will radiate it out into your yard. Your efficient wood burning appliance just got a lot less efficient. Hence, the blue circle in your plan would be perfect for any woodburning appliance as they only heat lost is the one going up the flue. The rest will heat your home sooner or later depending on how well you can distribute it.
Now to the difference between stove, fireplace insert, zero clearance fireplace: First, you don't need an insert as you don't have a masonry fireplace and I doubt you want to spend all that money to build one. A zero clearance fireplace is essentially a steelbox that has been designed to be installed into a woodframe. Here is a scheme:
You can buy units that are as inefficient as any masonry fireplace but also many that are as efficient as a modern woodstove. Check the efficiency ratings and whether it says "EPA-approved" or "EPA-certified" or similar (however, NOT EPA-exempt). As you can deduce from the picture, room air flows around the unit, heats up and is released in the top. If the blower would not be working you would need to rely on convection but no heat gets lost other than the one going up the flue. If the wall in the back goes to the outside, its insulation would determine how much heat you would lose there. However, that has nothing to do with your fireplace; the same would apply to a woodstove sitting there.
The FP30 I linked to earlier has the same firebox as the PE Summit but its outer shell is designed to be installed as a ZC fireplace. The efficiency is essentially the same. There are many other manufacturers who make efficient ZC fireplaces (KozyHeat, Lennox, Fireplace Xtraordinaire, Osburn, Napoleon, Valcourt, RSF etc.)
What you could do with that blue circle alcove is building it out of bricks or similar, then install a modern ZC fireplace facing the living room and finish that side, too. The fireplace will heat up the bricks which will radiate it into the entry. You get the effect of a masonry heater. Of course, you can also put up drywall if you like that better. Those modern ZC fireplaces can also be ducted meaning you can run a duct through the attic over the corridor and dump the heat somewhere between the laundry and the bedroom 2 to heat also that part of the house.