I’m sure this topic should be merged with one of those @AnotherElk has mentioned.
But for the FP3 as @BertG says there’s little or no complains about the battery being loose, and I have no problem with the little catches engaging.
So I’ve just checked, I do use a case. I removed the case and the back cover. I can moved the battery slightly by lifting it at the bottom but this dis not encourage the battery to fall out nor power down the phone. So I took an image of the battery cover.
This is for the FP3+ not the transparent cover of the FP3.
Note the back cover has varying thicknesses, contours, the lowest and therefore the thinnest is where the battery is, maybe this is to help cooling. To compensate for the lack of pressure on the battery from the case a surround of spongy plastic is added which presumably presses on the battery when the back cover is in place.