fix(shs-5958): fix private page tests #1150

Job	Run time
test_phpunit	1m 29s
set_sites	40s
lint_theme	42s
test_new_site	12m 43s
test_existing_site (aaai)	6m 35s
test_existing_site (buddhiststudies)	7m 7s
test_existing_site (default)	5m 35s
test_existing_site (facultyaffairs_humsci)	6m 7s
test_existing_site (hs_fcp)	6m 5s
test_existing_site (hs_fps)	5m 29s
test_existing_site (oconnell)	5m 47s
test_existing_site (siw)	6m 4s
test_existing_site (statistics)	9m 4s
test_existing_site (west)	8m 18s
deploy_branch	0s
	1h 21m 45s

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