Optimize Write Signature calculation (#5905) #8834

Job	Run time
lint	3m 42s
CodeQL	7m 53s
test	18m 4s
build	3m 54s
integration-configs-db	2m 0s
integration (requires_docker)	5m 38s
integration (integration_alertmanager)	3m 49s
integration (integration_backward_compatibility)	8m 55s
integration (integration_memberlist)	7m 28s
integration (integration_querier)	12m 10s
integration (integration_ruler)	4m 6s
integration (integration_query_fuzz)	2m 21s
deploy_website	44s
deploy	2m 29s
	1h 23m 13s

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