What are the rules for damage to worn magic items (non-weapon or armor)

I have a character who found a magic vest that enables the wearer to cast prestidigitation at will. The character wants to wear the vest into combat. I ruled that the vest, a loose-fitting item of clothing much thicker than a simple shirt wouldn’t fit under leather armor, so he wears the vest over his armor.

What are the rules for damage to magic items like this? Are they immune to typical types of non-magical damage delivered in combat? What about magical damage?

Or is it unreasonable to make him wear it outside his leather armor? That would make his decision seem less problematic, but even under armor, when characters take slashing, piercing, fire or acid damage in combat, the arrow or whatever would pierce the armor, and therefore the vest, at least some of the time. (Sometimes the hit might be in an unarmored part of the body.)

The only thing I could find is DMG p.141 “Most magic items, other than potions and scrolls, have resistance to all damage.” But it doesn’t say immunity, and if it has resistance (takes half damage) then that implies that it has some amount of damage it can take before being destroyed. And in the table of minor properties on p.143, one of the properties is unbreakable, implying that items without this property can be destroyed.

I could just be over-complicating things. I could ignore it and just let him wear the darn thing. It’d be too cumbersome to have to take it off before every combat. But I’m curious what other people have done.