Thank you for posting to the forums. You'll need to download the Creative Cloud desktop app to get your fonts: Adobe creative desktop apps | Adobe Creative Cloud. The Adobe Fonts team and the Adobe Stock team share some code and when we set up Font purchases this shared code causes the Font purchase to display as Adobe Stock On Demand in Account Management and under the invoices. It's an issue I've been working to resolve for some time.
If you decide to subscribe to any of our Creative Cloud products Adobe Fonts are included in your subscription. You can learn more here: About | Adobe Fonts