Add a login test against Synapse to Playwright (#11913)

* Install playwright

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Add foundations for writing tests under Playwright

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* .gitignore juggling

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Add tsconfig and fix eslint rules

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Add docker & synapse plugins

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Add login.spec.ts

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Wire up fixture which sets up ElementAppPage & bakes config.json

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Remove launch test, it has served its purpose

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Remove test which has been ported to Playwright

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Fix test not cleaning up after itself

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Move registerUser to the Homeserver interface

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Remove unused fixture param

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Remove redundant launch test

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>

* Add newline

---------

Signed-off-by: Michael Telatynski <7t3chguy@gmail.com>
Co-authored-by: R Midhun Suresh <hi@midhun.dev>

package.json

@@ -184,6 +184,7 @@
         "@typescript-eslint/parser": "^5.6.0",
         "allchange": "^1.1.0",
         "axe-core": "4.8.2",
+        "axe-playwright": "^1.2.3",
         "babel-jest": "^29.0.0",
         "blob-polyfill": "^7.0.0",
         "cypress": "^12.0.0",