What data does Iridex store?

Iridex stores what it needs to run the features you turn on, and nothing beyond that.

Activity stats — message and voice-time counts per member, for leaderboards. Not message content, unless ticket transcripts are switched on for that specific server.
Settings — whatever you configure on the dashboard for your server.
Account email — only if you've confirmed one (see turning on email notifications), used solely for account and security notices.

The full policy is at iridex.me/privacy.

Still stuck? Ask in the support server.