Enhance `cortex_ingester_inflight_push_requests` metric #10750

Job	Run time
CodeQL	7m 28s
CodeQL	7m 28s
lint	4m 18s
lint	4m 18s
build	4m 6s
build	4m 6s
test	13m 53s
test	16m 20s
test-no-race	7m 20s
test-no-race	7m 20s
integration-configs-db	2m 39s
integration-configs-db	2m 39s
integration (requires_docker)	7m 32s
integration (requires_docker)	7m 32s
integration (integration_alertmanager)	4m 13s
integration (integration_alertmanager)	4m 13s
integration (integration_backward_compatibility)	11m 2s
integration (integration_backward_compatibility)	11m 2s
integration (integration_memberlist)	7m 48s
integration (integration_memberlist)	7m 48s
integration (integration_querier)	13m 50s
integration (integration_querier)	15m 20s
integration (integration_ruler)	5m 36s
integration (integration_ruler)	5m 36s
integration (integration_query_fuzz)	4m 50s
integration (integration_query_fuzz)	4m 50s
deploy_website	0s
deploy_website	0s
deploy	1s
deploy	0s
	3h 13m 8s

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