With today's 62.2.A.0.428 update the on-screen keyboard hiding bug is still present. Very disappointing. Maybe it's just me, but this makes the gesture navigation mode nearly impossible to use.
I discovered that the issue only affects the bottom part of the bottom "bar" near the screen's edge. If you tap or tap and hold on the half that is closer to the edge of the screen, you can switch to the previous app, but it's not supposed to work like that.
So what happens when you tap the down arrow to hide the keyboard is that both the down-arrow gets pressed, and the bottom half of the bar is tapped as well, triggering the unwanted switch to the previously used app.
If you are very careful, you can tap the bottom part of the down-arrow so that the keyboard is hidden and the app is not switched.
On another note, I get the impression that the screen somehow looks even worse than with with the initial Android 13 release, which already looked worse than Android 12 to me. I'm talking about the infamous greenish hue / bit depth crushing effect.