eframe: Fix clicks in web (#3640)

Closes #3633

Bug introduced in #3623 (after 0.24.0 was cut)

crates/eframe/src/web/app_runner.rs

@@ -173,20 +173,8 @@ impl AppRunner {
         self.painter.destroy();
     }
 
-    /// Runs the user code and paints the UI.
-    ///
-    /// If there is already an outstanding frame of output,
-    /// that is painted instead.
-    pub fn run_and_paint(&mut self) {
-        if self.clipped_primitives.is_none() {
-            // Run user code, and paint the results:
-            self.logic();
-            self.paint();
-        } else {
-            // We have already run the logic, e.g. in an on-click event,
-            // so let's only present the results:
-            self.paint();
-        }
+    pub fn has_outstanding_paint_data(&self) -> bool {
+        self.clipped_primitives.is_some()
     }
 
     /// Runs the logic, but doesn't paint the result.

crates/eframe/src/web/events.rs

@@ -17,8 +17,25 @@ fn paint_and_schedule(runner_ref: &WebRunner) -> Result<(), JsValue> {
 
 fn paint_if_needed(runner: &mut AppRunner) {
     if runner.needs_repaint.needs_repaint() {
-        runner.needs_repaint.clear();
-        runner.run_and_paint();
+        if runner.has_outstanding_paint_data() {
+            // We have already run the logic, e.g. in an on-click event,
+            // so let's only present the results:
+            runner.paint();
+
+            // We schedule another repaint asap, so that we can run the actual logic
+            // again, which may schedule a new repaint (if there's animations):
+            runner.needs_repaint.repaint_asap();
+        } else {
+            // Clear the `needs_repaint` flags _before_
+            // running the logic, as the logic could cause it to be set again.
+            runner.needs_repaint.clear();
+
+            // Run user code…
+            runner.logic();
+
+            // …and paint the result.
+            runner.paint();
+        }
     }
     runner.auto_save_if_needed();
 }