AirTag won’t beep when I replace the battery

Are you using Duracell replacements?

Their “bitterant” coating inhibits functionality in AirTags.

Use non-bitterant coated batteries.

See note after the 1st para “3” in this article:

How to replace the battery in your AirTag - Apple Support

Note that you don’t get the “beep” until the AirTag’s metal cover is being replaced.

(not when the battery is first inserted)

Can you “play a sound” using FindMy on your iPhone?

Would tend to agree as the tag WAS working with the previous - albeit depleted - battery.