Upgrade to Catalina erased all data, have backups but how to restore applications/software? I had tried upgrading my MacBook Pro to Catalina from Mojave a couple of times on my own, but always got stuck on a 'could not be verified' error at the very end of downloading the said upgrade. Finally I decided to get it done at a verified Apple Service Centre. I have backups of my important documents on iCloud as well as a Time Machine backup for everything on an external hard disk.
I had submitted my MacBook Pro to the Service Centre yesterday and got it back today. The upgrade to Catalina is perfect, but I've lost all my data and applications. Even the user profile that I was using is nowhere to be found.
Now iCloud is automatically restoring some of the documents that I had backed up, but the applications/software that I had installed are completely lost. I do have a Time Machine backup, but I am not sure how I restore to that one. Moreover, restoring would take me back to OS Mojave, I think.
Is there any way I can keep Catalina but get back my applications/software from Time Machine?
The Migration Assistant is the program on any Mac that allows you to transfer in or out data and applications. I would connect your backup drive and then start the assistant.
It will then show you the information from the most recent backup or if there are many backups and the system can’t tell which backup was on your Mac, you can choose from the many destinations that can be saved to one Time Machine drive.
You can bring in accounts, settings, applications or a mix of some or all of the above.
Here is Apple’s support article that I think does a good job of the overall design and intent of this process.

https://support.apple.com/en-us/HT204350

Since Catalina has excellent support for containers, the old steps to reinvoke the assistant are a bit complicated. If you don’t have anything on your new system, erasing the content / reinstalling in an erase install might be much easier now that you are on Catalina.