You don’t spec the ESC by the battery, the motor dictates the ESC current you require. Motors draw current from the battery according to the load placed upon them, the greater the load, the more current they need to overcome the load and spin. In a plane the drag and mass of the prop moving through the air is the load. Bigger, steeper pitch prop turning faster = more load.
The motor will draw up to its maximum stall current until it cooks if the load is too great. Or until the smoke comes out the ESC or the battery runs flat, whichever comes soonest. Batteries do not PUSH current to the motors.
Think of the battery as a gas tank. The bigger the engine on the end, the more fuel it draws from the tank as you accelerate.
3000mah is large for a plane, most FT designs are set up to be light, easy to fly and use smaller packs. Picking a plane you like, then getting right pack for the planes size and weight distribution is much better and cheaper than having a huge battery and trying to fly it. Most lipo is under $20, half my FT fleet run off sub $10 packs. Even my 4s 100C quad packs were less than $20.
The motor is what counts, the motor and propeller combination will try and draw a certain number of watts and from that you can determine the amp draw using watts/volts = amps. look for the tables that get published with motors to find out the watts draw expectation then work out the amps and add 25% or so for a safety margin to spec your ESC.
EMAX 2205 red bottom 2300kv motor. Specs here https://www.emaxmodel.com/emax-rs2205-racespec-motor.html
for 3S (About 12 volts full charge) turning a 5 inch three blade prop with a 4 1/2 inch pitch will pull approx 248 watts
That's 248 watts divided by 12 is 20.6 amps, add 25% means you needs an ESC rated at around 25 amps.
To calculate the amps for any battery: mAh/1000 x C.
You can safely draw 90 amps from your battery (3,000/1,000 x 30)
Any Esc that draws 90 amps or less will work. A larger draw will harm the battery.
Pick a motor that will draw less amps than the Esc can supply. Leave a small overhead for the servos to draw. If your motor & servos draw more amp than the Esc can supply, you will fry the Esc.
It would be possible to use a larger Esc, say 100 amps. Provided your motor & servos don’t exceed what the battery can supply.
The amp rating for batteries & Esc are the maximum safe draw they can handle. They can be used is any application that doesn’t exceed the maximum.