If you live in an area with snow or rain, I think that a metal roof there is the only solution. That's a very shallow slope and wind-blown rain or ice dams are sure to cause problems with asphalt shingles.

Plus, unless visitors arrive by helicopter, they are never going to really see much (if any) of that shallow roof from the ground.

Métal for the entire roof or just for the dormer? Won’t an all metal roof be pricey?

You don't know what the price is until you request a formal quote from an installer. Yes, a standing seam roof is more than a shingle roof, but metal roofs are for a lifetime and don't burn.

https://www.remodelingimage.com/architectural-shingles-vs-standing-seam-metal-roof-cost/