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fix(tests): close three integration-test races that flaked CI #2098

Job	Run time
docs changes	24s
docs benchmark (${{ matrix.target }})	0s
docs source	4m 15s
docs build	2m 41s
docs acceptance (corpus)	2m 33s
docs acceptance (chromium)	2m 30s
docs acceptance (http)	2m 24s
docs acceptance (webkit)	2m 20s
docs HTTP	4s
	17m 11s