Web demo stops repainting after clicking

[YgorSouza]

Describe the bug

On the web demo, the UI stops repainting after you click anywhere, and only starts again when you move the mouse. Also, when you press Ctrl+C, it pauses for a fraction of a second. This does not affect the native desktop demo.

To Reproduce
Steps to reproduce the behavior:

1. Open the web demo
2. Select continuous mode or open something that is animated, like plot demo or the fractal clock
3. Click anywhere on the screen and leave the mouse completely still
4. The UI stops repainting until you move the mouse

Expected behavior

The UI should continue to repaint as normal after clicking or pressing Ctrl+C.

Screenshots

web_demo_click_bug.mp4

Desktop (please complete the following information):

• OS: Fedora 38, Windows 11
• Browser Firefox
• Version 120

Smartphone (please complete the following information):
(not tested)

Additional context

This seems to have been caused by #3623.

[abey79]

I believe this is the same as another phenomenon I just observed: collapsing header need the mouse to move around to complete animation:

egui_0.24_bug.mp4

[YgorSouza]

Yes, one effect of that is that all animations freeze when you click. My guess is that the click event resets the "needs_repaint" flag somehow, no matter how many widgets called request_repaint on that frame. And so it doesn't repaint again until it gets an input event. There are a lot of changes in that PR related to that, but I don't understand it well enough to see where the problem is.

Note that this bug is not in the 0.24 release AFAICT, as it was introduced yesterday just after the release.