Tooltips reappear after being closed

### Tested versions

Reproduced in v4.5.dev3.official [55fc6e73f], v4.4.stable.official [4c311cbee], v4.3.stable.official [77dcf97d8] and v1.0.stable.custom_build
(it says custom_build but it's the win64 binary I just downloaded)

### System information

Godot v4.4.stable - Windows 11 (build 22631) - Multi-window, 1 monitor - OpenGL 3 (Compatibility) - Intel(R) Iris(R) Xe Graphics (Intel Corporation; 32.0.101.5768) - 11th Gen Intel(R) Core(TM) i7-1185G7 @ 3.00GHz (8 threads)

### Issue description

This issue is concerned with the behaviour of tooltips and the rules that govern *when a tooltip should appear*. I've edited this issue in an attempt to clarify this.

When a tooltip is dismissed/closed (hidden in response to user input), *no user input is required to cause it to appear again*.
Specifically, tooltips will reappear without the mouse being moved at all.
The behaviour occurs in running projects as well as the editor and affects all versions of Godot, as far as I can tell.

The expected behaviour, and that of typical desktop software requires the cursor to exit the bounds of the element that triggered the tooltip, before the tooltip *is allowed* to be shown again. I say *"is allowed"* because the other rules still apply -- the rules that governed the initial appearance of the tooltip, i.e. mouse lingers over the element.

In the video, a tooltip for a node in the scene tree appears and I press the Escape key to dismiss it. The mouse/cursor is not moved (other than at the start/end). The tooltip reappears and Escape is pressed again. This is repeated several times.

https://github.com/user-attachments/assets/ffde8d68-5348-4782-ae75-9d1005d4f72c

### Steps to reproduce

1. hover mouse over node in scene tree
2. wait. a tooltip will appear
3. press escape to dismiss the tooltip
4. wait. a tooltip will appear

### Minimal reproduction project (MRP)

N/A

Reproduce the issue in the Godot editor by hovering a scene-tree node, dismissing its tooltip with Escape, and waiting without moving the cursor. Trace the tooltip handling from that interaction; done means a dismissed tooltip stays hidden until the cursor exits and re-enters the triggering element, while the existing appearance rules remain intact.

Written by the indexing model from the issue text.