Don't install playwright twice (#29302)

1. `playwright/test` is already installed as part of `deps-frontend` on
CI which runs before, so it's better to not install it again (on a
potentially different version), and just use the version from
package.json and add the `deps-frontend` dependency.
2. `PLAYWRIGHT_DIR` is a undefined variable, so I removed it

```bash
$ git show c8ded77680 | grep PLAYWRIGHT_DIR
+playwright: $(PLAYWRIGHT_DIR)
```

(cherry picked from commit c236e64aca42b9ab0743431bc505033a0cb78b93)

Makefile

@@ -625,8 +625,7 @@ test-mssql\#%: integrations.mssql.test generate-ini-mssql
 test-mssql-migration: migrations.mssql.test migrations.individual.mssql.test
 
 .PHONY: playwright
-playwright: $(PLAYWRIGHT_DIR)
-	npm install --no-save @playwright/test
+playwright: deps-frontend
 	npx playwright install $(PLAYWRIGHT_FLAGS)
 
 .PHONY: test-e2e%