Yes, thats 3600A, except its not its more AMP hours of time. Your bus must handle the current that will be drawn, not what you can feed it. IE the transformer that feeds your house probably can dump 500A, but you are wired for 200A to a 200A breaker in your panel. So you want to be able to hit a demand of 48KW with 48v batteries. You are going to need about 48000W/48V = 1000A + 20% is 1200A on your BUS BARS. You will want to fuse/breaker the feed wires from each battery rack appropriately based on the cable you connect to the bus with. So if you ran 4, 2pos+2neg say 4/0 cables from each rack to the bus bar, you would want a 300 or so amp breaker/fuse inline in each of the positive cables about 600A / rack. That way fuses blow if any load exceeds what your cable can handle. By the same token each of the units should draw/push no more than 300A. 1/0THHN is rated for 150A @ 75C, so two 1/0 from the inverter to the bus bars with 150A breakers inline with the positive cables. There are folks that recommend 125% on the breakers. You can do that but bump to 2/0 wire, noting a 150A breaker should actually run at 5-10% overcurrent for a few minutes, but should not run over 80% for more than a few hours. You should really not ever have anything close to a 200A demand on your panel. I would be surprised if you hit 150A, assuming you have two 4T AC's and your house is all electric. It is rare for everything to be on at the same time, and unheard of for it to all stay running that way for any length of time.
It sounds like you want to fully power a 200A panel. I'm basically doing something similar with a pair of 18K's. I just posted a jpg of my wiring diagram, in a different post. I'm using a 6x6 raceway, and I just ran flex conduit down to the tray. My setup is feeding a transfer switch that is running a 100A panel that is feeding my house. My house is about 1400 sqft, and all electric, I have a single roof mounted 4T A/C, it pulls around 18A, I also have two (2) EV's that I charge, currently using time of use rates. The amount of current down a 4/0 cable seems to be a rather fluid number depending on who you talk to. I've got *one* rack/30 KW of batteries. I've been monitoring my per-leg demand for about the last 4 months with some modbus sensors and an SBC. My mean draw at night is around 12 or so amps (12x240 = 3KW). . . So that 30K of battery should theoretically get me around 10 hours. Figure 6-8 hours for a reality check,we shall see.
The problem is going to be getting enough solar to charge the batteries, and run your loads. As someone in another thread reminded me in Phoenix we get about 6 hours equivalent of direct sunlight at best, so with my 14KW of panels I'm going to net 14KW*6HRS = 84KWH of power/day. Now I'm going to be tapping some of it, directly during the day, and the actual window for the 84KWH is wider than 6 hours, sun comes up where we might see some trickle of juice around 0600, and drops below the horizon around 1900, but that puts me at a minimum of 11 hours of ZERO PV juice. The plan would be to supplement the batteries with off-peak nitetime juice from the grid, until the sun comes up. I may break down and get another rack of 6, but I doubt I would go up to three. Each 5KWH will deliver 50v/100A, so two racks will get you to your 48KW in terms of demand. Adding more is about time. The other problem is the wiring pain goes up exponentially at the number of inverters. You should try and keep your battery wires roughly the same length, so when you have 4 units, you are going to end up looping some of the wires to the inverters closest to the bus. The battery wires and bus bars are going to set you back a big chunk of change.
You might check your electric bill and divide your total kwh by days in your billing cycle. On my worst bill I used about 3500KWH in August (or July, one of them) last year, that's about 116KWH/day... Conclusion: I need more panels before I need more batteries

YMMV. It would be pretty slick if I could tap the batteries in my EV's over the long night. This is supposedly coming at some point. I did set up my PV DC/Surge breaker panel to handle 6 strings, I'm only starting with 4, but I want to bring it up to about 20KW with 16 more panels somewhere. Then I might worry about more batteries.