What happened to “Other” storage on my Mac?

The short answer

Apple renamed it. Since macOS Monterey (version 12), what used to show as Other shows as System Data. It holds the same things: caches, logs, app data, browser files, developer tools and macOS's own working files. If Other was big before you updated, System Data is big now for the same reasons.

What moved into System Data

App and browser caches
Chat app files from Slack, Teams, WhatsApp and Discord
Time Machine local snapshots
Developer folders: Xcode, Docker, Gradle, npm
Logs, memory swap and other macOS working files

Everything on the System Data page applies to Other too, including what's safe to clear and what to leave alone.