Most AVRs can only handle up to 3 zones, so you will likely need an AVR for the home theatre room and then a whole home audio system for the other areas. For a project that size and considering that it's a new build, I would also recommend a professional installer working with your contractor.
Looks like you have an open concept living and kitchen area. That does not lend itself well to home theatre. You have no place for rear speakers unless on stands right behind the couch (or on a long table behind the couch) and for side surrounds the bay window will present a problem. If you have cathedral ceilings then proper locations for ATMOS speakers could be an issue as well. For rooms like that it is often better to go with a good 3.1 or 3.2 setup and maybe some height speakers if you can't place the surrounds at ear level. For 7.1.4 you want a rectangular room not open to the kitchen and with normal ceiling height. For open concept rooms a few good speakers can work better than a lot of poorly placed speakers.
