"Everyone is very tired today."
は doesn't necessarily mark the subject (the thing doing the action) though, it marks the topic to clarify what you're talking about, or to show contrast. These things can also happen to be the subject, but they don't have to be.
That being said, I think that you could have perfectly grammatical sentences with みんなは, but in the case of this sentence you're most likely talking about how today is different from other days, which is why you'd say きょうは. It's kind of like the difference between, "What's up with today, everyone's tired for some reason" (きょうは), as opposed to, "EVERYONE is tired today, instead of just some people" (みんなは).
Here's an article I read that helped me understand the difference between は and が better: https://8020japanese.com/wa-vs-ga/
Why not 今日、みんなすごく疲れてる ? Other exercises involving "みんな" haven't needed topic/subject particles...
Oh, 今日はみんなすごく疲れてる isn't accepted either. But it does accept "今日はみんなすごく疲れています", not sure what on earth the difference is (for every other exercise the plain form equivalent is accepted).