The hardware has gone up in 2022, almost 2023. 1K is much too low to be dealing with a skilled cabinet maker for this. The whole ensemble there is easily 15-20K when built and finished by a custom cabinet maker with the right tools and experience. For paint grade. Stained wood would have species upcharges.

Barn door? If you don't mind seeing the washer and dryer, you could install a panel to cover the hot water heater and just unscrew it when you need access, which you probably won't need very often.

Agreed with latest comment- lay out where your sofa/accent chairs will go and think about best traffic flow for the door opening. I would think a slider opening left to right would be most convenient for kids and guests so they‘re not tracking though the middle of the living room. Also consider where the view will be when the doors are fully open. We have a similar layout and wish the doors were pocket-like or accordion style so we don’t have any frame blocking the view out our. Since you dont have a lot of wall space on either side, maybe you could do accordion style. Highly recommend since it makes indoor-outdoor space feel SO much bigger - great for parties with the deck space you have! Also, we took the screens off. Makes it feel twice as open!

So by reading "throughout" and "online calculator per room" that infers that you are just going to put a grid of recessed lights everywhere. No consideration for furniture placement, doors/windows, function, mood or aesthetics. Many choose to do just that and if that is your goal, carry on. Seeing the rooms or ceiling height aren't big factors between choosing 4" vs 6", that choice would pertain to spacing, cost, and aesthetics. And the fact that they are wafers is more about installation method than lighting layout, as they have pros and cons just like any other type of recessed lighting you choose. But if a lighting designer were choosing, a grid of lighting would not be the solution everywhere. As an example, in the Living Room, That would not fit the seating layout or mood of the space. Instead, a couple accent lights over the fireplace, maybe over a feature wall too, layered with table lamps would be a better choice. And removing the existing center flush mount. Another example is the Kitchen/Dining, where the existing chandelier over the table is perfect, no recessed needed. The Kitchen could have recessed to replace the 2 flush mounts and provide task light over the counters and into cabinets, but a general grid does not usually line up with the task functions, that is better to be based on cabinet/counter/island locations. For bedrooms, a recessed light in each corner usually creates a hot spot over the bed, attracting attention to a dead nook created by a dresser, or an unbalanced wall wash caused by a window interruption. So without some architectural features, any recessed would be more uncommon.