Grafana (Cloud version) doesn't send notifications when Alert rule is fired

Your alert should have preview routing, where you can see which notification policy is catching your alert.
Unified (not old obsolete legacy) alert is event based - firing event generates event with labels and then based on labels you define which contact point will be triggered in notification policy - that’s complex, but powerful concept (but many people has a problem to understand it, so that simplified routing was also introduced), e.g. os=linux => send email to linux support group, priority=p1 => send text message to CTO, …