/v1/support-requests lets you create and manage inbox conversations from your own systems — useful if support requests originate somewhere other than email or chat (an in-app form, for instance).
Support requests created via the API link to a contact automatically, the same as any other conversation, so they show up in Contacts and the inbox alongside everything else — API-created conversations aren't a separate, siloed thing.
Create, list, get, reply to, and patch (update status, assignee, etc. on) requests, all from the same set of endpoints.