test: improve resilience of asset timestamp E2E test #1426

Job	Run time
lint	2m 7s
build	10s
e2e_windows (windows-2025, 22, npm, 1)	35s
e2e_windows (windows-2025, 22, npm, 0)	38s
e2e_windows (windows-2025, 22, npm, 3)	32s
e2e_windows (windows-2025, 22, esbuild, 5)	28s
e2e_windows (windows-2025, 22, esbuild, 2)	38s
e2e_windows (windows-2025, 22, esbuild, 3)	34s
e2e_windows (windows-2025, 22, esbuild, 0)	39s
e2e_windows (windows-2025, 22, esbuild, 4)	35s
e2e_windows (windows-2025, 22, npm, 5)	33s
e2e_windows (windows-2025, 22, esbuild, 1)	31s
e2e_windows (windows-2025, 22, npm, 4)	38s
e2e_windows (windows-2025, 22, npm, 2)	34s
e2e	0s
test	0s
Browser Compatibility Tests	0s
publish-snapshots	0s
e2e-package-managers	0s
e2e-snapshots	0s
	9m 12s

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