Tests: Move the HTTP response codes test for consistency. #5716

Job	Run time
${{ ((matrix.multisite && 'Multisite') \|\| 'Single Site') }} ${{ ((matrix.memcached && 'Memcached') \|\| 'Default') }}	0s
matrix.label	-1s
Failed workflow tasks	-1s
Slack Notifications	-1s
Determine Matrix	-10s
	-13s

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