Good, you are creating a vault / pit larger than the spa to accommodate getting it in and out, and for any reason, like service or moving to a new home. I have been there where the spa was 92" square and the recess was 96" square. The owner expected access to be "my" problem. He wasn't happy with reality.
You are going to deck around the spa for a flush level fit, that's good. One thing to consider is what you are going tot do with the cover. You will have a 12" height from deck to top of the spa, IF it were 24" you could simply fold the cover in half and teeter tauter the cover in a standing position with easy access to pull it back down on top of the sp to close, just a thought.
My suggestion was to put steps in front of the spa, flower boxes around the corners, and side bars at the upper level of the spa on which to place trays for beverages or what snacks. Maybe even a pergola over the top for hanging baskets. IF you ever have to access anything from the side or lower reaches of the spa, you can easily pull away the steps, side bars, flower boxes etc. This may only affect 20% of the spas installed, so it’s up to you to figure if you are in the 80% or the 20% of people in life that have to deal with it.
As for entry into the spa, at 12" you are stepping down into the water hole, will it be flat or slopped as foot begins to accept the weight of the body; keep in mind there is nothing to "grab" onto to keep your balance or equilibrium, especially something to think about for invited quest.
You concept of recessing it is to remove the large object from sight for a pleasing esthetics. Just don't paint yourself into a corner.
The “wizard”, who overruled my suggestions once, installed his spa recessed at the basement level walk out, with an 18 foot slope 30' back in his back yard. Get the picture. He was the "builder" and he wasn't open minded about changing his point of view, because he installed a sump pump in the recess to insure against any accumulation of water. Before construction was complete, the sump plugged up with construction debris, and that was when he found out that the 1,000 pound object actually floated, plus it was winter and it all froze as he hadn’t moved in yet.
I only found out in the spring when he wanted me to change out the electrical components under warranty because some wouldn't work and the pumps were screeching. The plumber and the building inspector filled me in as to what happened. Now I must admit, this is the only customer that I have never talked to again, because he got mad with me after I repaired everything and gave him the bill he know was coming, imagine that, he never paid the bill either. There is a price we all pay for education.