I just purchased a perpetual license for Office 2021 for the express purpose of using Publisher. Would this be considered a LTSC?
The LTSC version is a volume license, intended for (large) organization such as businesses. It is not a valid consumer (home use) license.
To run Publisher, you will need Office Professional 2021. Finding such a license today, when it is no longer sold by Microsoft, may be a challenge, though. Be very careful so that you don't buy a fake product key from a scammer.