Is this Time Machine change with Big Sur correct?

I have a new MacBook Pro with Big Sur. I use an external drive for some documents and up to now Time Machine was backing up my external drive without problems. I could not get Time Machine with Big Sur to backup my external drive. I called Apple Support and they told me that Big Sur has changed Time Machine and that now it can only backup the internal hard drive.

This sounds to me a little incredible, that is, that the new OS would set such a limitation to a good functionality of the previous one. I just want to verify that in your experience this reply by Apple Support is correct and that I now need to use a third party backup application.

Thanks for your time.