test: run frontend unit tests in browsers (#38860)

Run them in headless [vitest browser
mode](https://vitest.dev/guide/browser/) in chromium and firefox.
Similar UX than current tests, it's about 5 times as slow (goes from 1s
to 5s on my machine), but definitely worth it as it removes all
happy-dom problems.

---------

Signed-off-by: silverwind <me@silverwind.io>

.github/workflows/files-changed.yml

@@ -73,8 +73,9 @@ jobs:
             frontend:
               - "*.ts"
               - "web_src/**"
-              - "tools/generate-svg.ts"
-              - "tools/generate-svg-vscode-extensions.json"
+              - "tools/**/*.ts"
+              - "tools/**/*.json"
+              - "tools/playwright.sh"
               - "tsconfig.json"
               - "assets/emoji.json"
               - "package.json"
@@ -134,6 +135,7 @@ jobs:
             e2e:
               - "tests/e2e/**"
               - "tools/test-e2e.sh"
+              - "tools/playwright.sh"
               - "playwright.config.ts"
 
             shell:

.github/workflows/pull-compliance.yml

@@ -77,6 +77,7 @@ jobs:
       - run: make deps-frontend
       - run: make lint-frontend
       - run: make checks-frontend
+      - run: make playwright
       - run: make test-frontend
       - run: make frontend