AirTag not sounding with new battery

Try using a battery without a bitterant coating (Duracell batteries have it, so avoid this brand). The coating interferes with the AirTag.

FWIW, some Duracells w/ Bitterant coatings ARE “Compatible w/ AirTags” …

… and are explicitly so-marked on their packaging.

(Sometimes sold on the same rack w/ incompatible Duracells)

I suspect other manufacturers may also be doing the same.

How to replace the battery in your AirTag - Apple Support

TagSaver, Panasonic or Evergreen would be good choices. The ones that came with my AirTags are Panasonic.