chore: improve account name selection flow #6780

Job	Run time
test	3m 5s
code_style (lint)	2m 44s
code_style (prettier)	1m 59s
code_style (typecheck)	2m 9s
code_style (build:sample-apps)	4m 35s
code_style (danger)	1m 50s
ui-test / Playwright Tests (1, 5)	7m 49s
ui-test / Playwright Tests (2, 5)	8m 31s
ui-test / Playwright Tests (3, 5)	12m 16s
ui-test / Playwright Tests (4, 5)	8m 7s
ui-test / Playwright Tests (5, 5)	7m 55s
ui-test / setup_playwright_runners / setup-runners	42s
	1h 1m 42s

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