Wondering if anyone had issue with garlic burning. I want to use dark sheet pan for mushrooms but wonder if parchment or light pan makes more sense.

I think it's not the pan, but the format and duration of roasting the garlic.
Suggest either roast whole cloves for last 10-15 minutes, then squeeze out on mushrooms.
Or don't roast garlic at all, and add minced or grated to mushroom dish after cooking.
Roasting chopped garlic 45 minutes in any pan is likely to burn. Unless the original writer had a special technique we don't know about.