Alert processing rules, formerly known as Azure Monitor action rules are now generally available, following the public preview release in December 2021. This means that existing preview APIs of alert processing rules and action rules will be retired In June 2022, so environments need to be updated accordingly.
Alert processing rules allow you to apply processing to fired alerts. This differs from rules that create alerts such as Azure Monitor alert rules, as alert processing rules modify the fired alerts as they occur.
Full updated documentation is available here: Alert processing rules for Azure Monitor alerts. This contains use cases, rule properties and a how-to guide on configuring and managing alert processing rules.