[FSSDK-12089] move /public directory to /vitest/ (#1127) #1503

Job	Run time
browser_tests (chrome)	8m 11s
lint	1m 49s
unit_tests (18)	2m 35s
unit_tests (20)	2m 14s
browser_tests (safari)	4m 59s
lint_markdown_files / lint	1m 10s
unit_tests (22)	2m 3s
unit_tests (24)	1m 58s
integration_tests / test	8s
browser_tests (edge)	8m 47s
browser_tests (firefox)	10m 1s
fullstack_production_suite / test	6s
Coveralls coverage	5s
	44m 6s

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