Inside a LFP battery is a controller called a BMS that balances the cells, shuts off charging when too cold, and limits the discharge current among other things. Most bog standard LFP batteries have a BMS that's limited to 100a of discharge current at whatever voltage. So if you have a 12v 100Ah battery with a 100a BMS, the maximum it can discharge is 12v * 100a = 1200w of power. For a 24v system with 100a BMS batteries that would be 24v * 100a = 2400w maximum power. If you connected that to a 3000w inverter and loaded it up running the hot plate, the hair dryer, the TV, and the MargaritaMaster-9000 at the same time the BMS's would shut off the batteries output at 2400w before your inverter could reach its peak 3000w.
Most rackmount batteries are 48v but have that same 100a limitation, but 48v * 100a = 4800w of power which is more than enough for your 3000w inverter, but not enough to feed a 6000w inverter.
The ways around that are to either A: find a battery that has a 200 or 250a BMS built in doubling your wattage capacity (24v * 200a = 4800w, 48v * 200a = 9600w) which are a little more difficult but still available, OR B: get multiple batteries to help spread the load (2x batteries * 24v * 100a = 4800w, 2x batteries * 48v * 100a = 19,200w) which is what many people end up doing, especially if they're connecting bog standard 12v batteries together to get up to 24v or 48v systems.
Not quite. The split phase units like the MPP 6048 units are double the standby of a MPP 3048 because it's just 2 of the 3048's in the same box. The 6Kw units draw about double what a 3Kw unit draws, but EG4, MPP, and Growatt 3Kw-ish units all draw about the same standby wattage. It's mostly a factor of how big the inverter is, not the voltage base.
You could do 24v and a 3Kw inverter, but you wouldn't be able to use Trophy batteries (or almost any rackmount style) as they're only available in 48v and if you ever wanted to upgrade your system you'd have to change battery setups to 48v to get over 3Kw for the most part.