That gets a little complicated. If this were my money, I would use 100 amps, but I don't want you thinking I'm saying yes, so I recommend you do it.
I think its more important to figure out the draw off the battery in amps prior to connecting the device to the BMS. This would be the wattage you got off the killawatt meter / your inverter low voltage cutoff. My low voltage cutoff is 10.5 volts and mulitply that by 1.15 to account for inverter losses. Whatever that is will probably come out to about 1000 watts. That is also the most I would put on that inverter. There's some slop built into this, like its unlikely your voltage will sag that low, but you don't know until you plug it in and try it. If it doesn't sag that low, you still want to not change the low voltage cutoff because if you turn that on when the battery is in a low state of charge, it may then.
Class T fuses will not blow at its rated rating, its a combo of how long the current flows at how strong:
View attachment 56160
So with this chart, if a 125 amps are flowing across the fuse for 500 seconds will blow it, but still can run 200 amps through it for about a minute before it blows.
I think the limitation in your SOK is no more than 100 amps discharge. There's probably a BMS inside that shuts the battery down at that rate. One BMS I looked at had 110% the rated discharge rate for 5 seconds. I don't know what SOK uses. I also don't know how bad it is for the SOK battery to discharge at the 100 amp rate tripping this device. Maybe its not just the BMS tripping, but things inside melting. When I've had questions like that, I email whatever company tech department, and they are good at answering, and if no response, then I call.
I have a battery monitor, and I can watch how many amps my device pulls. I do not worry about amperage on my 12 volt system at all except for a couple of items. First, the 500 watt K-Cup coffee maker at 55 amps. Second, the Vacuum (800 watts?) at 75 amps. Those two would be fine to run off the battery one at a time. The last one is the 1200 watt microwave, that actually pulls 2100 DC watts at 155 amps. That would not be able to run off the battery because of the battery 100 amp limitation, but would run for at least a minute before the fuse blew. So the 100 amp fuse would not protect you from tripping the 100 amp battery cutoff. If you did a calculation fuse to blow quicker before the BMS kicks in, then it gets ridiculously small.
That total 100 amps for the battery is also a bit hard to calculate. When I have my propane heater on, it pulls 9 amps form the battery. It comes on when it gets cold throughout the night. There's also draw of certain things like .5 amps for my stereo, .5 amps to run my propane fridge. That goes into the 100 amp limit, not just the one high wattage item.
Overall, I still feel by putting that 100 amp fuse in my system protects me from when I walk away from the RV, and someone decides to run the microwave for 2 minutes. If the battery doesn't shut off, then before the time is up on the microwave, the fuse will blow.
What I'm telling you some will say is way too much, but I bet there will be a lot less likelhood of having an electric fire.
EDIT: I do not have a fuse between the bus bar and the inverter, only between the the battery and the busbar. I'm not sure why you put one there unless your inverter manual says to do so.