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In their offer email, Michigan states that it is not their practice to "compete" with offers from other schools. Can anyone confirm whether this is true, or whether should one still try to negotiate with them?

I don't think it could hurt. But you might want to stay away from the word 'negotiate.' In general, I don't think admissions at any school would react well to that

They don't negotiate, but they wouldn't necessarily object to hearing about offers from other schools and might just decide to increase your scholarship amount.

Anecdotally, people have had success with this.

If you haven't already, you should look through the Michigan c/o 2019 thread and the Negotiating Scholarships thread. They contain some useful information on this topic.