Can’t reconnect air tag after replacing battery

In practice, just replacing the AirTag's battery should not cause it to unpair with your iPhone. I'm assuming that you replaced the battery with one that does not use a bitterant coating and it was a CR2032 coin-type battery.

Have you tried any of the following:

• Tried removing & replacing the battery again?
• Tried using another "known good" battery?
• Tried resetting the AirTag?

It will depend on the battery manufacturer. For example, Duracell coin batteries tend to have bitterant coatings. You just need to shop around to find those that don't. I suggest trying an Internet search for C2032 batteries without a bitterant coating.

If the AirTag doesn’t emit a “beep” as soon as the cover is placed on the new battery …

… it likely HAS the coating.