Replace winapi with windows-sys crate (#7416)

This the second take of <https://github.com/emilk/egui/pull/5038>,
adjusted for newer version of `windows-sys`, and with merge conflicts
resolved. I added the original author to `Co-authored-by:`.

* Closes <https://github.com/emilk/egui/issues/7334>
* Closes <https://github.com/emilk/egui/pull/5038>
* [x] I have followed the instructions in the PR template

Tested on Windows 10:
<img width="322" height="272" alt="image"
src="https://github.com/user-attachments/assets/15ddf0bf-1f30-452f-8764-07ccfce2b00c"
/>
<img width="802" height="632" alt="image"
src="https://github.com/user-attachments/assets/db6f4586-cfa5-4f7f-996c-06f7e2489df6"
/>

Action run result:
https://github.com/sola-contrib/egui/actions/runs/16748810761

---------

Co-authored-by: Casper Meijn <casper@meijn.net>

Cargo.lock

@@ -1242,7 +1242,6 @@ dependencies = [
  "web-sys",
  "web-time",
  "wgpu",
- "winapi",
  "windows-sys 0.59.0",
  "winit",
 ]