Add ViewportInfo::occluded and visible (#7948)

* Part of https://github.com/emilk/egui/issues/5112
* Part of https://github.com/emilk/egui/issues/5113
* Part of https://github.com/emilk/egui/issues/5136

Once we support calling `App::logic` when an app is occluded or
minimized, it is useful to know that it is, in fact, occluded or
minimized.

---------

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

tests/test_background_logic/Cargo.toml

@@ -0,0 +1,14 @@
+[package]
+name = "test_background_logic"
+version = "0.1.0"
+license = "MIT OR Apache-2.0"
+edition = "2024"
+rust-version = "1.92"
+publish = false
+
+[lints]
+workspace = true
+
+[dependencies]
+eframe = { workspace = true, features = ["default"] }
+env_logger = { workspace = true, features = ["auto-color", "humantime"] }

tests/test_background_logic/src/main.rs

@@ -0,0 +1,64 @@
+#![cfg_attr(not(debug_assertions), windows_subsystem = "windows")]
+#![expect(rustdoc::missing_crate_level_docs)]
+#![allow(clippy::print_stderr)]
+
+use std::time::Duration;
+
+use eframe::egui::{self, ViewportInfo};
+
+fn main() {
+    env_logger::init();
+
+    let _ = eframe::run_native(
+        "Background Logic Test",
+        eframe::NativeOptions {
+            viewport: egui::ViewportBuilder::default().with_inner_size([400.0, 200.0]),
+            ..Default::default()
+        },
+        Box::new(|_cc| Ok(Box::new(App))),
+    );
+}
+
+struct App;
+
+impl eframe::App for App {
+    fn logic(&mut self, ctx: &egui::Context, _frame: &mut eframe::Frame) {
+        eprintln!("App::logic called {}", viewport_info(ctx));
+        ctx.request_repaint_after(Duration::from_secs(1));
+    }
+
+    fn ui(&mut self, ui: &mut egui::Ui, _frame: &mut eframe::Frame) {
+        eprintln!("App::ui called {}", viewport_info(ui.ctx()));
+        ui.centered_and_justified(|ui| {
+            ui.heading("Minimize this window");
+        });
+    }
+}
+
+fn viewport_info(ctx: &egui::Context) -> String {
+    ctx.input(|i| {
+        let ViewportInfo {
+            minimized,
+            focused,
+            occluded,
+            ..
+        } = i.viewport();
+
+        let visible = i.viewport().visible();
+
+        let mut s = String::new();
+
+        let flags = [
+            ("focused", focused),
+            ("occluded", occluded),
+            ("minimized", minimized),
+            ("visible", &visible),
+        ];
+        for (name, value) in flags {
+            if let Some(value) = value {
+                s += &format!(" {name}={value}");
+            }
+        }
+        s
+    })
+}