I have several door handles .. and interior side is OK ... but exterior
has dulled badly.
https://flic.kr/p/27WZ4dC

These are presumably brass (can't be 100% certain) at least look & feel
like.

It will take some effort to polish back up ..... are there any good
finishes that will protect them.
I remember doing this on a previous house - bought spray on clear cote
lacquer - didn't last 1 winter.