We need more details on what happened to reach this point including how you were upgrading macOS (including version of the installer and whether you erased a volume). Or do you mean you installed a Catalina security update?
Many times users install a new version of macOS onto the incorrect APFS volume causing temporary loss of data (in theory) since the data should still exist on the old APFS volume which may now be a read-only system volume. Do you have multiple " - Data" volumes shown in Disk Utility? It may look something like "Macintosh HD", "Macintosh HD - Data", and "Macintosh HD - Data - Data". If so, then your data may be on the "Macintosh HD - Data" volume. I honestly don't know what the macOS installer does to the data on a " - Data" volume. If this is the case, then the volume should be mounted under "Volumes". Within the Finder click on the "Go" menu and type "/Volumes" without the double-quotes. This should allow you to see those other volumes that macOS/Finder typically hides from users.
Or did you run out of storage space when upgrading macOS?
If the SSD has been erased, then you will be unable to recover the data unless you had a backup before things went wrong. If the T2 firmware is corrupted or the Logic Board is bad, then there is no way to recover the data since the data is encrypted by the hardware that is controlled by the T2 chip.
If the laptop is not booting due to an OS related issue, then you may be able to reinstall macOS, but some of the methods may require you to "Revive" or "Restore" the T2 firmware (the latter "Restore" will destroy all the data on the SSD).
Revive or restore an Intel-based Mac with Apple Configurator 2 - Apple Support
You may need to take the laptop to Apple or an Apple Authorized Service Provider for assistance as it may require someone to actually see the laptop in order to tell if it is possible to access the data. If they cannot assist you, then you will need to contact a professional data recovery service such as Drive Savers or Ontrack to see if they can retrieve your data. Both vendors provide free estimates and both are recommended by Apple.
You should always have frequent and regular backups. There are many situations where it is impossible to recover data from an SSD and a USB-C Mac, but especially from a T2 Mac since the data is encrypted by the T2 security chip which requires the Logic Board to be functional (or made functional again).