refactor: update local storage keys #6110

Job	Run time
Bundle size check	2m 25s
code_style (lint)	2m 27s
test	2m 3s
code_style (prettier)	1m 45s
code_style (typecheck)	2m 10s
code_style (build:sample-apps)	2m 46s
ui-test / Playwright Tests (1, 5)	11m 26s
ui-test / Playwright Tests (2, 5)	8m 49s
ui-test / Playwright Tests (3, 5)	7m 9s
ui-test / Playwright Tests (4, 5)	7m 53s
ui-test / Playwright Tests (5, 5)	8m 42s
ui-test / setup_playwright_runners / setup-runners	51s
	58m 26s

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