Optimize Write Signature calculation #8831

Job	Run time
test	17m 58s
CodeQL	7m 48s
build	4m 12s
lint	3m 46s
integration-configs-db	2m 0s
integration (requires_docker)	5m 42s
integration (integration_alertmanager)	3m 59s
integration (integration_backward_compatibility)	7m 50s
integration (integration_memberlist)	7m 50s
integration (integration_querier)	11m 53s
integration (integration_ruler)	4m 11s
integration (integration_query_fuzz)	2m 23s
deploy_website	0s
deploy	0s
	1h 19m 32s

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