test: add fallback for Playwright-provided browser #8708

Job	Run time
Build Java and TypeScript for other tasks	3m 13s
Check style	2m 10s
Test Java	3m 13s
Gradle tests (ubuntu-latest)	3m 52s
ITs (ubuntu-latest, group-1)	4m 56s
Gradle tests (windows-latest)	7m 44s
ITs (ubuntu-latest, group-2)	5m 25s
Test TypeScript	1m 20s
ITs (ubuntu-latest, some)	4m 36s
Tests Summary	2s
	36m 31s

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