test: improve login tests #4458

Job	Run time
Generate SDKs	1m 7s
Run Playwright end-to-end tests (postgres)	11m 52s
Run Playwright end-to-end tests (cockroach)	12m 6s
Run tests and lints	23m 49s
Run Playwright end-to-end tests (sqlite)	11m 53s
Run end-to-end tests (postgres)	44m 12s
Run Playwright end-to-end tests (mysql)	12m 1s
Run end-to-end tests (cockroach)	47m 31s
Run end-to-end tests (sqlite)	45m 16s
Run end-to-end tests (mysql)	44m 32s
Build CLI docs	1m 34s
Generate changelog	0s
Generate release	0s
Render version schema	0s
Draft newsletter	0s
Release SDKs	0s
Pending approval Slack notification	0s
Send newsletter	0s
	4h 15m 53s

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