tests(e2e): improve login util stability #27623

Job	Run time
build (node: 20)	4m 29s
pretty (node: 20)	1m 45s
changes	23s
typescript	3m 4s
unit_front (node: 20)	4m 30s
unit_back (node: 18)	2m 18s
unit_back (node: 20)	2m 10s
lint (node: 20)	4m 48s
CLI Tests	1m 55s
[CE] e2e (browser: chromium)	10m 41s
[CE] e2e (browser: webkit)	10m 0s
[EE] e2e (browser: chromium)	14m 1s
[CE] e2e (browser: firefox)	13m 44s
[EE] e2e (browser: webkit)	24m 3s
[EE] e2e (browser: firefox)	16m 11s
[CE] API Integration (mysql:latest, package: mysql2}, node: ${{ matrix.node }}, shard: ${{ matrix.shard }})	0s
[CE] API Integration (postgres, node: ${{ matrix.node }}, shard: ${{ matrix.shard }})	0s
[CE] API Integration (sqlite, package: better-sqlite3, node: ${{ matrix.node }}, shard: ${{ matrix.shard }})	0s
[EE] API Integration (mysql:latest, package: mysql2, node: ${{ matrix.node }}, shard: ${{ matrix.shard }})	0s
[EE] API Integration (postgres, node: ${{ matrix.node }}, shard: ${{ matrix.shard }})	0s
[EE] API Integration (sqlite, client: better-sqlite3, node: ${{ matrix.node }}, shard: ${{ matrix.shard }})	0s
	1h 54m 2s

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