> The “Follow” button is visible when I take the screenshot mid-switch.

Does this indicate that the privacy feature has a gap, where you could reveal the length of your password if you take a screenshot mid app switch?

No because per default the input is not cleared when screenshotting. If you‘d implement this yourself for security reasons you'd most likely blur / overlay the whole screen when the app enters background state.

Probably, but to the extent that was at all a problem to begin with, multiply it by another 0.0001 or whatever for the threat of the screenshot being taken mid switch away!