The test says "connection timed out"

Your web host is most likely blocking outgoing connections on that port; some hosts, DigitalOcean among them, block 25, 465 and 587 altogether. The test tries the other ports your mail service publishes straight away, a few seconds each and at most 15 seconds in all, and says which one answered. Many services publish 2525 for exactly this case. Press Use port 2525 (or whichever port it names) and send the test again. Nothing changes until you press it. With Encryption set to None, no other port is tried, and the result says so.

If no port answers, the result says which ports were tried. Ask your host whether it blocks outgoing connections to your mail server, and which port it allows; some will open one, and the ones that will not usually offer their own mail service instead. From the command line, wp email-delivery test me@example.com --ports tries the same ports and changes nothing.