Furthermore, worn items can’t be broken in DND. Ever. As in that sword wouldn’t have shattered.

...that's not true tho?

a mundane sword, indeed all mundane objects, can be broken!

there's a section with a table (DMG chapter 8; objects) with AC, HP, and so forth for objects of various sizes and materials.

it's also on the starterpack DM screens!

the sword in question would have 3d6 HP and AC 19.

the relevant rules section, directly above said tables, isn't very helpful in general, but it clearly says that all objects can, in principle, be destroyed:

[...] given enough time and the right tools, characters can destroy any destructible object. Use common sense when determining a character's success at damaging an object.

DnD isn't really made for complex equipment maintenance, so it's perfectly reasonable to completely ignore these rules in normal play...which is why it's one of those things everyone always forgets about...

what, afaik, actually can't be broken are magic items. at least I'm pretty sure according to the rules they're not meant to ever be broken...

edit: it's artifacts that usually can't be destroyed; magic items are just described as "at least as durable as a regular item of it's kind", but resistant to ALL damage...

as for the heat metal with adamantine skin interaction...dunno, I'd say it depends on whether the adamantine is right on the surface of the skin or not: magic in DnD is pretty well established to not work inside of a creatures body, with very few, explicitly stated, exceptions (because it would allow all sorts of dumb loopholes, like control water, a cantrip, being able to freeze blood inside a living being...that would obviously be broken, so magic stops at the skin, usually)