Can an old iPad 2 run a purchased Etsy planner app?

The digital planners that I see for sale on Etsy, are essentially PDFs that would get imported into a ‘smart’ annotation app, such as Goodnotes, Notability, Noteshelf, Zinnia, ZoomNotes, Xodo (limited), etc. These app names come from the Etsy description pages.

The latest versions of these annotation apps require iPadOS 17.5, 17.0, 16.0, 15.5, 11.0, 16.0 or later, respectively.

Check which of these apps have a version available on an iOS/iPadOS 12 device, through the on-device App Store. Some of these app developers may not sell old versions of their apps in the App Store.

If the Etsy app you purchased did not specify the OS restrictions, then all you can do is try. We cannot answer that question. But it is likely your old iPad will not support it as it is quite old.