refactor: local storage keys to appkit + network switch fixes #6171

Job	Run time
Bundle size check	2m 27s
test	2m 9s
code_style (lint)	2m 33s
code_style (prettier)	1m 46s
code_style (typecheck)	1m 58s
code_style (build:sample-apps)	3m 17s
ui-test / Playwright Tests (1, 5)	7m 11s
ui-test / Playwright Tests (2, 5)	7m 39s
ui-test / Playwright Tests (3, 5)	6m 45s
ui-test / Playwright Tests (4, 5)	7m 54s
ui-test / Playwright Tests (5, 5)	9m 24s
ui-test / setup_playwright_runners / setup-runners	50s
	53m 53s

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