Full format erases files off a drive too (but it is not a secure erase). Using the drive maker's toolset you can always do a sector scan anyway or use something like HDTune that does the same thing anyway but the maker's tools are the preferred option. In all these decades of computering I have not once needed to do a full format on any drive.
With a new drive the first thing I do is check the SMART values, power on time to make sure it's not a previous returned drive put into a freshly sealed box etc, and to make sure not errors are reported. Then do a sector health check in HDTune Pro or in the case now as my internal drives are Samsung, using Samsung Magician which has a diagnostics feature that scans. These scans take about 30 seconds or less for even an 8TB drive which is all the peace of mind I need to know a drive is in solid working order.