ci: Streamline CI browser playwright tests (#13276)

This PR streamlines our browser integration tests a bit more:

1. We now only install chromium for playwright tests in most places.
This may help cut down test run time a bit, as we do not need to install
native dependencies for webkit and firefox everywhere.
2. I changed how we split the matrix jobs for the browser integration
tests. Previously, we sharded this via playwright. Now, we only do this
for esm tests, which we now only run in chromium, not all browsers. Only
the full bundle tests are run in all browsers (they are considerably
faster than the esm tests...), and there we now do not use sharding, but
have one matrix job for chromium (default), one for webkit and one for
firefox (where each can only install the native dependencies it needs).
3. I renamed the jobs a bit so that we can see a bit more of the job
name in the Github UI... it still truncates but you see more than
before, at least...
4. For all other playwright tests (e.g. e2e tests etc) we only install
chromium, AFAIK we do not have any non-chromium tests anywhere there.

Some data points:
* E2E tests seem to be about 10-20% faster than before, by looking
through traces here:
https://sentry.sentry.io/performance/trace/c5c1c643f1db0e8dd97df658405c2035/?field=title&field=event.type&field=project&field=user.display&field=timestamp&name=All+Events&node=txn-8892bc908791478aba163dd3edd373b4&project=5899451&query=&sort=-timestamp&source=discover&statsPeriod=1h&timestamp=1723118364&yAxis=count%28%29
* For the playwright steps it's a bit harder to say as they are renamed,
also they are not super consistent in execution time, we'll have to
monitor it a bit afterwards, but subjectively it appears a bit shorter
in most cases too.

.github/actions/install-playwright/action.yml

@@ -1,5 +1,9 @@
 name: "Install Playwright dependencies"
 description: "Installs Playwright dependencies and caches them."
+inputs:
+  browsers:
+    description: 'What browsers to install.'
+    default: 'chromium webkit firefox'
 
 runs:
   using: "composite"
@@ -17,12 +21,13 @@ runs:
             ~/.cache/ms-playwright
           key: playwright-${{ runner.os }}-${{ steps.playwright-version.outputs.version }}
 
+      # We always install all browsers, if uncached
       - name: Install Playwright dependencies (uncached)
         run: npx playwright install chromium webkit firefox --with-deps
         if: steps.playwright-cache.outputs.cache-hit != 'true'
         shell: bash
 
       - name: Install Playwright system dependencies only (cached)
-        run: npx playwright install-deps chromium webkit firefox
+        run: npx playwright install-deps ${{ inputs.browsers || 'chromium webkit firefox' }}
         if: steps.playwright-cache.outputs.cache-hit == 'true'
         shell: bash

.github/workflows/build.yml

@@ -528,7 +528,7 @@ jobs:
         run: yarn lerna run test --scope @sentry/profiling-node
 
   job_browser_playwright_tests:
-    name: Playwright (${{ matrix.bundle }}${{ matrix.shard && format(' {0}/{1}', matrix.shard, matrix.shards) || ''}}) Tests
+    name: Playwright ${{ matrix.bundle }}${{ matrix.project && matrix.project != 'chromium' && format(' {0}', matrix.project) || ''}}${{ matrix.shard && format(' ({0}/{1})', matrix.shard, matrix.shards) || ''}} Tests
     needs: [job_get_metadata, job_build]
     if: needs.job_build.outputs.changed_browser_integration == 'true' || github.event_name != 'pull_request'
     runs-on: ubuntu-20.04-large-js
@@ -548,31 +548,30 @@ jobs:
         project:
           - chromium
         include:
-          # Only check all projects for esm & full bundle
+          # Only check all projects for full bundle
           # We also shard the tests as they take the longest
           - bundle: bundle_tracing_replay_feedback_min
-            project: ''
-            shard: 1
-            shards: 2
+            project: 'webkit'
           - bundle: bundle_tracing_replay_feedback_min
-            project: ''
-            shard: 2
-            shards: 2
+            project: 'firefox'
           - bundle: esm
-            project: ''
+            project: chromium
             shard: 1
-            shards: 3
+            shards: 4
           - bundle: esm
+            project: chromium
             shard: 2
-            shards: 3
+            shards: 4
           - bundle: esm
-            project: ''
+            project: chromium
             shard: 3
-            shards: 3
+            shards: 4
+          - bundle: esm
+            project: chromium
+            shard: 4
+            shards: 4
         exclude:
-          # Do not run the default chromium-only tests
-          - bundle: bundle_tracing_replay_feedback_min
-            project: 'chromium'
+          # Do not run the un-sharded esm tests
           - bundle: esm
             project: 'chromium'
 
@@ -592,12 +591,15 @@ jobs:
 
       - name: Install Playwright
         uses: ./.github/actions/install-playwright
+        with:
+          browsers: ${{ matrix.project }}
 
       - name: Run Playwright tests
         env:
           PW_BUNDLE: ${{ matrix.bundle }}
         working-directory: dev-packages/browser-integration-tests
         run: yarn test:ci${{ matrix.project && format(' --project={0}', matrix.project) || '' }}${{ matrix.shard && format(' --shard={0}/{1}', matrix.shard, matrix.shards) || '' }}
+
       - name: Upload Playwright Traces
         uses: actions/upload-artifact@v3
         if: always()
@@ -606,7 +608,7 @@ jobs:
           path: dev-packages/browser-integration-tests/test-results
 
   job_browser_loader_tests:
-    name: Playwright Loader (${{ matrix.bundle }}) Tests
+    name: PW ${{ matrix.bundle }} Tests
     needs: [job_get_metadata, job_build]
     if: needs.job_build.outputs.changed_browser_integration == 'true' || github.event_name != 'pull_request'
     runs-on: ubuntu-20.04
@@ -639,6 +641,8 @@ jobs:
 
       - name: Install Playwright
         uses: ./.github/actions/install-playwright
+        with:
+          browsers: chromium
 
       - name: Run Playwright Loader tests
         env:
@@ -750,8 +754,12 @@ jobs:
         uses: ./.github/actions/restore-cache
         env:
           DEPENDENCY_CACHE_KEY: ${{ needs.job_build.outputs.dependency_cache_key }}
+
       - name: Install Playwright
         uses: ./.github/actions/install-playwright
+        with:
+          browsers: chromium
+
       - name: Run integration tests
         env:
           NODE_VERSION: ${{ matrix.node }}
@@ -953,6 +961,8 @@ jobs:
 
       - name: Install Playwright
         uses: ./.github/actions/install-playwright
+        with:
+          browsers: chromium
 
       - name: Get node version
         id: versions
@@ -1050,6 +1060,8 @@ jobs:
 
       - name: Install Playwright
         uses: ./.github/actions/install-playwright
+        with:
+          browsers: chromium
 
       - name: Get node version
         id: versions
@@ -1150,6 +1162,8 @@ jobs:
 
       - name: Install Playwright
         uses: ./.github/actions/install-playwright
+        with:
+          browsers: chromium
 
       - name: Get node version
         id: versions