tests: Move quart under toxgen #3400

Job	Run time
Flags (pinned) (3.9, ubuntu-22.04)	1m 43s
Flags (pinned) (3.12, ubuntu-22.04)	3m 42s
Flags (pinned) (3.7, ubuntu-22.04)	1m 43s
Flags (pinned) (3.13, ubuntu-22.04)	4m 5s
Flags (pinned) (3.8, ubuntu-22.04)	2m 18s
All pinned Flags tests passed	2s
	13m 33s

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