Unable to "reconnect" time machine backup

My Airport Extreme suddenly disappeared from my network along with the backup USB drive plugged into it (thanks for the bug, Apple). I unplugged and restarted the airport and it showed up again. But now time machine is not recognizing the existing backup - it wants to start all over and backup the entire 350GB instead of "reconnecting" to the existing backup and adding to it as it usually does.

I don't want to lose the old backups nor wait 3 days while it painfully does the entire backup. Is there a fix?

BTW, I'm so frustrated with Apple these days. I wish I was not deeply locked into the ecosystem. Does anybody else remember the days when Apple made easy to use software that was not deeply buggy? I do. I guess I'm old.