This is different enough from your situation that it may not be helpful, but just in case there are ideas of use:
My 90-something MIL is in pretty good shape but suffering from MCI, and we've set her up with an iPad to use exclusively for incoming FaceTime calls. She is not technically capable, so is not the same boat as your sister, although she has learned to answer an incoming call which is all that's necessary for this case. That it works pretty much like a phone has helped--the concept of answering the thing that is ringing was easy enough to grasp and hold on to. It's sync'd to her hearing aids, so she can hear when we're calling if she's wearing them, and if not the ringer is at max volume so she can generally hear it ringing. No lock code at all since that's beyond her capability, and everything else is locked down to prevent mis-taps.
With one of the magnetic covers it auto-sleeps when closed and auto-wakes when opened, so that mostly takes care of accidental app opening and such (no need to understand the power button), and combined with one of those magnetic USB-C cable adapters, even with arthritis she can connect and disconnect it from the charger without much difficulty.
This setup has worked surprisingly well for the past several years. Having a regularly scheduled call time has helped a lot in this case, since she gets herself prepared when she's expecting a call.
I have remote access turned on, and while it's something of a chore to get her to tap the "accept" button twice, I have managed to do long-distance troubleshooting a couple of times that way.
I'll note that it depends a lot on ear condition, but getting that thing connected to her hearing aids was a game-changer--it's functionally impossible to communicate with her otherwise, but she can generally hear pretty well on a call with them in and connected to the iPad.
If the goal was purely FaceTime, that setup might work for you, but since you're trying to give your sister more capability, it's oversimplified. It also doesn't address the hiding stuff issue you're dealing with, which has not been an issue with my MIL since she has learned to just keep it in its home beside the landline and plugged in when not in use.
Again, if you were purely after FaceTime, and there aren't hearing aids involved, maybe just the ringer sound would lead her to a hidden/misplaced iPad, if she were nearby. Better still if you have a scheduled call time that she remembers, so she'd either look for it or be ready to answer when called.
I feel like a fundamental issue with whatever you come up with is going to be charging, though; if she's hiding things and losing track of them, then it doesn't matter what means you provide to find them, once the battery dies none of those will help.