You cannot approach it from the GE panel side, their answer will always be the same: GE. From the standpoint of any panel manufacturer, they NEVER list their panels to be used with anything other than their own breakers. Why would they?
But from a BREAKER manufacturer's standpoint, you WANT to list your breakers in competitive panels, IF YOU CAN, and if it is economically feasible. To get a breaker listed in a competitive panel, you must test it with EVERY possible panel that the original breakers were listed in. On average, the testing cost is around $25,000 per line item, per test. So let's say that GE makes 20 different panels that their THQP breakers work in. If Sq. D wants to sell a Homeline breaker that can be UL listed to plug into any GE panel that would accept a THQP, that means $25K per breaker (frame), per GE panel. So assuming at least 2 breaker frames in residential plug-ins (typically 15-60A and 70A and above, even if they look the same on the outside), that is 40 tests at $25K each; $1,000,000 in UL testing costs! You have to be able to sell a LOT of replacement breakers to afford that.
But people do it all the time, there is a lot of demand for "interchangeable" aftermarket breakers, as evidenced by the Chinese trying to counterfeit them all the time. So you need to look at the breakers themselves to see if they SPECIFICALLY say they are UL listed to work in YOUR SPECIFIC panel, there are no short cuts. Plus you must be ready to prove it, with documentation, to an AHJ if he asks.
PS: UL kind of talks out of both sides of their mouths on this issue. From the PANEL side, they will say that the panel must be listed with the specific breakers, so that will be the panel mfr's burden and they will only list it with their own products. But at the same time, UL allows BREAKERS to be listed in other panels, as long as someone does the above testing. In essence they kind of contradict themselves, but it's been that way for decades now.