There are two ways you could download:
Manually, using a web browser, from your account at https://affinity.store/account/downloads and if you did that they are wherever you downloaded them.
Or automatically, via the new My Account dialog. If you did that, they were downloaded to a temporary location and automatically installed. In that case, where you find them depends on what they were. Assets would be in the Assets studio panel. Templates (if in .aftemplate format) would be found via File > New in the Templates part of the dialog.
The My Accounts dialog will tell you whether something is downloaded or not, and what kind of object it was.