How do I test a GFCI circuit breaker (without pushing the "test" button)?
They do make testers but it depends on where you live to the model used.
I will guess you are in the US since this is a new requirement.
The good thing about us power is the max voltage to ground is 120v
240v is 2 120v lines that are out of phase so the max voltage to ground is 120v where other places in the world have 240v to ground.
I have a fancy one that plugs into a wall socket and a precision 10 turn pot so I can verify from 3ma to 100 ma depending on the type of protection required (personal or equipment),
According to the NEC commentary in the handbook GFCI’s for personal protection is required the set points are from 4-6 ma  you can do like I did with my 180$ tester and turn it into a 4 wire tester with a receptacle and a plug mounted in a box (ok the first few times I did it I just used wires on the prongs but you can use a standard tester with an adapter to test Connecting the smaller prong (hot) to one of the hot(s) and the ground round pin on the tester to the ground on the stove receptacle
When the test button is pressed a 15.5k resistor is connected from ground to a hot this is above the 4-6 at almost 8 ma but a good test unless you want to purchase the pro model and record the exact trip point I have a switch on my setup so I can test both hot’s after checking 5 or 6 they all trip at the exact same level no matter which hot is connected.
I used a standard 120v receptacle single a single pole double throw switch And a 50 a 4 wire range power cord , plug my tester in and push the button on the cheap home owner one or dial the resistance until it Tripp's this fit in a single gang box with a 3/4 cord grip. I have not seen a commercially available tester so I made one that will work with either of my standard receptacle testers.
If you really want to test this was the cheapest way I could find to do it.