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>

crates/eframe/Cargo.toml

@@ -192,11 +192,12 @@ objc2-app-kit = { version = "0.2.0", default-features = false, features = [
 
 # windows:
 [target.'cfg(any(target_os = "windows"))'.dependencies]
-winapi = { version = "0.3.9", features = ["winuser"] }
 windows-sys = { workspace = true, features = [
   "Win32_Foundation",
-  "Win32_UI_Shell",
   "Win32_System_Com",
+  "Win32_UI_Input_KeyboardAndMouse",
+  "Win32_UI_Shell",
+  "Win32_UI_WindowsAndMessaging",
 ] }
 
 # -------------------------------------------