feat: enhance Playwright configuration and improve test coverage #384

Job	Run time
playwright-tests (mongo, dev)	5m 4s
playwright-tests (postgres, dev)	5m 33s
playwright-tests (postgres, bundle)	4m 20s
playwright-tests (sqlite, bundle)	4m 58s
playwright-tests (sqlite, dev)	4m 37s
playwright-tests (mongo, bundle)	5m 38s
	30m 10s

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