Remove Tooltip mouse tracker listener & update hovering/MouseRegion logic & animation (#119199)

Fixes https://github.com/flutter/flutter/issues/117627

### Behavior changes:
1. If fade in/fade out animation is already in progress, hiding/showing the tooltip will immediately take effect without waiting for `waitDuration`.
2. A PointerDownEvent that doesn't become a part of a "trigger" gesture dismisses the tooltip, even for hovered ones.
3. The OverlayEntry is now updated only when the previous tooltip was completely dismissed. This can be fixed by OverlayPortal but I'm not sure what the correct behavior is.

examples/api/test/material/tooltip/tooltip.3_test.dart

@@ -20,7 +20,8 @@ void main() {
     await tester.tap(find.byType(FloatingActionButton));
     await tester.pump(const Duration(milliseconds: 10));
     expect(find.text(tooltipText), findsOneWidget);
-    // Wait for the tooltip to disappear.
+    // Tap on the tooltip and wait for the tooltip to disappear.
+    await tester.tap(find.byTooltip(tooltipText));
     await tester.pump(const Duration(seconds: 1));
     expect(find.text(tooltipText), findsNothing);
   });

packages/flutter/lib/src/painting/geometry.dart

@@ -49,14 +49,14 @@ Offset positionDependentBox({
   final bool fitsBelow = target.dy + verticalOffset + childSize.height <= size.height - margin;
   final bool fitsAbove = target.dy - verticalOffset - childSize.height >= margin;
   final bool tooltipBelow = preferBelow ? fitsBelow || !fitsAbove : !(fitsAbove || !fitsBelow);
-  double y;
+  final double y;
   if (tooltipBelow) {
     y = math.min(target.dy + verticalOffset, size.height - margin);
   } else {
     y = math.max(target.dy - verticalOffset - childSize.height, margin);
   }
   // HORIZONTAL DIRECTION
-  double x;
+  final double x;
   if (size.width - margin * 2.0 < childSize.width) {
     x = (size.width - childSize.width) / 2.0;
   } else {

packages/flutter/test/material/checkbox_test.dart

@@ -1610,9 +1610,12 @@ void main() {
       )
     );
 
-    final Finder tooltip1 = find.byType(Tooltip);
+    await tester.pump(const Duration(days: 1));
+    await tester.pumpAndSettle();
     expect(find.text(tapTooltip), findsNothing);
+    expect(find.text(longPressTooltip), findsNothing);
 
+    final Finder tooltip1 = find.byType(Tooltip);
     await tester.tap(tooltip1);
     await tester.pump(const Duration(milliseconds: 10));
     expect(find.text(tapTooltip), findsOneWidget);

packages/flutter/test/material/radio_test.dart

@@ -1250,9 +1250,12 @@ void main() {
       )
     );
 
-    final Finder tooltip1 = find.byType(Tooltip);
+    await tester.pump(const Duration(days: 1));
+    await tester.pumpAndSettle();
     expect(find.text(tapTooltip), findsNothing);
+    expect(find.text(longPressTooltip), findsNothing);
 
+    final Finder tooltip1 = find.byType(Tooltip);
     await tester.tap(tooltip1);
     await tester.pump(const Duration(milliseconds: 10));
     expect(find.text(tapTooltip), findsOneWidget);

packages/flutter/test/material/switch_test.dart

@@ -1835,9 +1835,12 @@ void main() {
       )
     );
 
-    final Finder tooltip1 = find.byType(Tooltip);
+    await tester.pump(const Duration(days: 1));
+    await tester.pumpAndSettle();
     expect(find.text(tapTooltip), findsNothing);
+    expect(find.text(longPressTooltip), findsNothing);
 
+    final Finder tooltip1 = find.byType(Tooltip);
     await tester.tap(tooltip1);
     await tester.pump(const Duration(milliseconds: 10));
     expect(find.text(tapTooltip), findsOneWidget);