The Slack app posts new conversations and replies into a Slack channel and lets a team respond or get notified without leaving Slack, which is the most commonly installed app for internal visibility. The Mailchimp app syncs contact data so audiences built in Intercom can be used for email campaigns in Mailchimp without a manual export. The broader App Store covers dozens of smaller integrations, mostly aimed at getting contact and event data flowing between Intercom and whatever marketing or analytics stack a team already runs.
Intercom and Zendesk, on the other hand, don't have a deep native integration, and that's not an oversight. They compete directly for a lot of the same support and messaging use cases. What shows up in that search is usually one of two real situations: a business running both for different purposes (Intercom for chat and sales messaging, Zendesk for ticketing) that needs a custom connection between them, or a business actually migrating from one to the other and needing to move data across, not integrate the two long-term.