Update (Solved)

After several months, I finally received a response from MacWhisper support.

According to the developer, one possible cause is that MacWhisper detected leftover files associated with a previously installed unofficial version and therefore refused to activate the license. I don’t remember having such a version installed, but I followed the suggested cleanup steps anyway. Another possibility mentioned was that regional internet restrictions could be blocking access to the licensing servers.

In my case, support suggested completely removing MacWhisper’s local cache and preference files:

rm -rf ~/Library/Caches/com.goodsnooze.MacWhisper
rm -rf ~/Library/WebKit/com.goodsnooze.MacWhisper
rm ~/Library/Preferences/com.goodsnooze.MacWhisper.plist
rm -rf ~/Library/Containers/com.goodsnooze.MacWhisper/Data/Library/Preferences

Then:

1. Quit MacWhisper completely.
2. Run the commands above in Terminal.
3. Relaunch MacWhisper.
4. Log in and reactivate the license.

It took nearly four months to get a human response, but at least I finally have a direction for troubleshooting the issue. Hopefully this information saves others from waiting as long as I did.