You need a long, public, audit-ready track record for a transactional email API today. The established names in transactional email have it; unsent.dev is earlier in its public arc. If procurement requires three years of public uptime data and a multi-language SDK matrix on day one, use one of those. Come back when an emerging option is acceptable.
Your traffic is bulk marketing or campaigns. Different primitive, different platform. See Cold Email Outreach for outbound prospecting through your own mailboxes, or a marketing-campaign tool with templates and list management for newsletters. unsent.dev is for transactional traffic.
You want SMTP, not HTTP. Use Outbound SMTP directly. The API and the relay are siblings on the same delivery stack, not replacements. Pick the surface that matches your team. The mail goes out the same pipe.