I'll let Oscar chime in, who has taken the lead on the Midnight Enigma page. But I believe the "Recently Transmitted Messages" at the bottom of the page may have been encrypted with an actual Enigma simulator. But even the "broken" ones, where most key settings are give, do not specify the rotor start positions. (Or may specify them, mislabeled as "Ring" settings, but then lack the actual ring setting?) So it's still not an easy task to decipher them.
The historical Enigma messages found on the internet are mostly (all?) German plaintext for obvious reasons. I can understand that non-German users are typically not keen on that additional level of deciphering... so we better get Midnight Enigma off the ground soon!
For what it's worth, when I asked ChatGPT about Enigma practice messages in English (hoping for some web references), it generated some for me! The key settings looked complete and plausible right away, for an Enigma I, including the historically correct 10 plugboard connections. But decoding the messages initially resulted in gibberish. When I complained about that, it generated new messages which decoded correctly!
I am not generally a fan of "look what AI told me" posts, but was quite impressed by this. When asked, ChatGPT explained that it had programmed an Enigma simulator in Python behind the scenes to generate the example messages. So, if you are into this kind of stuff, it's a neat way of playing with old and new technology at once.
Cheers,
Jürgen