docs: Improve README.md for clarity, detail, and structure #8936

Job	Run time
CodeQL	6m 51s
build	4m 44s
test	18m 32s
lint	16m 23s
integration-configs-db	2m 11s
integration (requires_docker)	5m 36s
integration (integration_alertmanager)	3m 57s
integration (integration_backward_compatibility)	8m 37s
integration (integration_memberlist)	7m 31s
integration (integration_querier)	11m 47s
integration (integration_ruler)	4m 8s
integration (integration_query_fuzz)	2m 19s
deploy	0s
deploy_website	0s
	1h 32m 36s

Provide feedback