https://discord.io/ has been replaced with a termination notice, and they directly mention where the credentials are being sold. Google the name, it's the top result.
Leaked credentials are sold on the open internet, on sites indexed by search engines. This isn't some quadruple proxy Anonymous hacker TOR exclusive club.
Edit: One better - any time you hear Microsoft, or Google, or Crebs, talking about some new "advanced" "Russian" "APT", 9 times out of 10 it's a kid posting on one of these forums, reselling stale credentials, or a fork of Mirai, or some other totally non-credible threat.
This stuff is WAY less cool than people make it seem.
1. confirming the emails were not already listed in other databases / leaks;
2. going to the actual Discord platform and performing a "Forgot Password" request, entering a stolen email, and seeing if it goes through or not, as Discord confirms if an email exists or not during this flow;
3. contacting Discord.io directly, who confirmed & put out a statement.
Other data breaches are harder to verify. Troy Hunt (owner of haveibeenpwned.com) described this in far more interesting ways than I ever could[0], but for each breach, it varies.
[0]: https://www.troyhunt.com/heres-how-i-verify-data-breaches/