My current company was something I would have considered endgame at the start of my career. Now it's not.
A company I'd consider to be currently endgame (say, FAANG), may not be 10 years later.
For the sake of discussion, as I mentioned in my original comment, I would simply define an endgame company as one where I'd be satisfied staying for a while without further ambition about finding the next great thing. Where I'd be content doing a helluva great job and not even think about leetcode.
My best friend ended up at one of the FAANGs a few years ago and is doing exactly that. Although he is now afraid that his leetcode skills have atrophied and he'd fail interviews horribly if for whatever (involuntary) reason he ends up having to look for another job. But he has no short term intention of leaving and thus hasn't been grinding leetcode for a while.
My wife's best friend thought it stupid (actually, I agree - it is stupid). Then she started dating a SWE, who is apparently also leetcoding in his spare time.
Unless you're close to retirement and don't really need the money, it's unlikely you'll know when you're there. Companies change and/or get into trouble, managers change, projects get canceled, etc. I've been at companies I spent quite a few years at and I still came close to quitting for various reasons (and eventually did). I'd submit there is no predictable endgame over more than a 2-3 year time horizon.