Replace cypress with playwright (#1988)

## Launch Checklist

This PR replaces cypress with playwright.
<img width="1907" height="933" alt="image"
src="https://github.com/user-attachments/assets/b52075b3-eb3b-45dc-93dc-8c5e9cfd35dd"
/>

I hope this will make the end-to-end debugging and fixing easier due to
the async await support of playwright which is missing in cypress.

This is a pure refactoring change.

 - [x] Briefly describe the changes in this PR.
 - [x] Add an entry to `CHANGELOG.md` under the `## main` section.

---------

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-authored-by: Copilot Autofix powered by AI <62310815+github-advanced-security[bot]@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

e2e/fixtures/rectangles-style.json

@@ -0,0 +1,92 @@
+{
+  "version": 8,
+  "sources": {
+    "rectangles": {
+      "type": "geojson",
+      "data": {
+        "type": "FeatureCollection",
+        "features": [
+          {
+            "type": "Feature",
+            "properties": {},
+            "geometry": {
+              "type": "Polygon",
+              "coordinates": [
+                [
+                  [
+                    -130.78125,
+                    -33.13755119234615
+                  ],
+                  [
+                    -130.78125,
+                    63.548552232036414
+                  ],
+                  [
+                    15.468749999999998,
+                    63.548552232036414
+                  ],
+                  [
+                    15.468749999999998,
+                    -33.13755119234615
+                  ],
+                  [
+                    -130.78125,
+                    -33.13755119234615
+                  ]
+                ]
+              ]
+            }
+          },
+          {
+            "type": "Feature",
+            "properties": {},
+            "geometry": {
+              "type": "Polygon",
+              "coordinates": [
+                [
+                  [
+                    -48.515625,
+                    -54.97761367069625
+                  ],
+                  [
+                    -48.515625,
+                    36.5978891330702
+                  ],
+                  [
+                    169.45312499999997,
+                    36.5978891330702
+                  ],
+                  [
+                    169.45312499999997,
+                    -54.97761367069625
+                  ],
+                  [
+                    -48.515625,
+                    -54.97761367069625
+                  ]
+                ]
+              ]
+            }
+          }
+        ]
+      }
+    }
+  },
+  "layers": [
+    {
+      "id": "background",
+      "type": "background",
+      "paint": {
+        "background-color": "white"
+      }
+    },
+    {
+      "id": "rectangles",
+      "type": "fill",
+      "source": "rectangles",
+      "paint": {
+        "fill-opacity": 0.3
+      }
+    }
+  ]
+}