Are there any birds with hair or fur versus feathers?

Bats - but they are mammals not birds.

Bats

Bats ain't no birds. Kiwis have sort of hairy feathers instead of feathery feathers, but otherwise all birds are feathered. Except for a few exceptions like frozen chickens.... Definitely no furry birds on this planet.

Also, once a year Geese will shed all their feathers and be "naked" for a short period of time.

https://www.ducks.org/conservation/waterfowl-research-science/understanding-waterfowl-the-amazing-molt

Birds have 'hair' and they are called rictal bristles, which are hairlike feathers that occur mostly around the base of the bill, nostrils and eyes.

These rictal bristles are modified from contour feathers in that they are without vanes. The word 'rictal' comes from 'rictus' which refers to the gape of the mouth. The function of the bristles occurring around the mouth is to increase the effective use of the gape (e.g. flycatchers and barbets). Eye bristles function as protective eyelashes (e.g. ostriches and hornbills) while bristles over the nostrils filter dust from the air.

However scientists in the past have traced the development of such bristles to that of feathers and they are not to be confused with the hair of mammals. So we call the outer covering for birds as feathers, mammals we call hair, and fish we call scales.
https://www.jstor.org/stable/4160198?seq=1#page_scan_tab_contents