3000 ac watts / .85 conversion factor / 24 volts low cutoff = 147.058823529 service amps
147.058823529 service amps / .8 fuse headroom = 183.823529412 fault amps
That means a minimum fuse size of 183ish amps.
The fuse is meant to protect the wire so you need wire rated for at least 183 amps.
For pure copper wire with insulation rated for 105 Celsius the smallest size that can handle 183 amps is 2 awg.
Since 2 awg can handle ~210 amps I suggest a 200 amp fuse.
The next readily available size is 0 awg which can accommodate a 250 amp fuse.
We have not talked about voltage drop which should also be considered.
For that we need to know the round trip circuit length.
Then we can use this calculator
https://www.calculator.net/voltage-drop-calculator.html to make sure the voltage drop is less than 3%.