Catalina update from Mojave: how to continue the download from where it was?

As far as I'm aware this is not possible, the update process gets interrupted and the temporary download gets removed.

This is inefficient, but due to the tool softwareupdate being apple proprietary there is no at home fix for this. To prevent this from happening in the future, you might be able to download the update manually with wget from a server that supports download continuation. (Most webservers these days)
But unless you're heavily starved on a data cap, just restarting the download from start saves you from a headache

Out of curiosity, considering you asked this 5 months ago, have you still not updated yet?

Nevertheless, here's my answer:

As far as I'm aware, if the connection is lost, the software update is cancelled, and there usually is no easy way to restart from where it was lost. A cancellation by definition usually involves the loss of progress.

I suppose, however, that there may be some obscure method by which this might be possible (I see a few comments which have various suggestions), but to be honest, its far more reasonable to simply redo the update than to take the risk to tamper with the software which runs your Mac, especially during a major MacOS update. Its simply not worth taking the risk to save 30 minutes.

I'm sure many people have had this sort of issue and wanted to do this before and if it was that simple Apple probably would've already made it so that you could start off from where you left. This suggests that it is not, so stay on the safe side.

Conclusion

So conclusion - maybe there is some complicated method which would do this, but my advice: don't risk it, just take a few extra minutes and you'll be safe, rather than sorry.