chore: balance e2e shards load (#45661)

## Problem

We run the e2e tests across two shards to reduce their duration.
However, one takes longer than the other.

## Solution

Use a currently hidden Playwright feature to balance their load

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

* **Chores**
* Upgraded Playwright test dependency to a newer version for refreshed
test tooling and fixes.
* Adjusted end-to-end test shard weighting to rebalance distribution
across parallel runs.

* **Tests**
* Stabilized several end-to-end editor interactions to make E2E flows
more reliable.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

.github/workflows/studio-e2e-test.yml

@@ -103,10 +103,10 @@ jobs:
         if: steps.filter.outputs.studio == 'true'
         run: SKIP_ASSET_UPLOAD=1 NODE_ENV=test NODE_OPTIONS="--max-old-space-size=4096" pnpm run build:studio
 
-      - name: 🚀 Run Playwright tests against Vercel Preview
+      - name: 🚀 Run Playwright tests against local studio build
         if: steps.filter.outputs.studio == 'true'
         id: playwright
-        run: pnpm e2e --shard=${{ matrix.shardIndex }}/${{ matrix.shardTotal }}
+        run: PWTEST_SHARD_WEIGHTS=62:38 pnpm e2e --shard=${{ matrix.shardIndex }}/${{ matrix.shardTotal }}
 
       - name: Upload blob report to GitHub Actions Artifacts
         if: always() && steps.filter.outputs.studio == 'true'