Refresh failing on dataset containing 2 Azure SQL databases

I recently added a second Azure SQL database to an existing dataset which is hooked up to another Azure SQL database, but now my refresh keeps failing. Before adding the 2nd database my reports had been refreshing without issue for the last 6 months.

The refresh history shows a failure message of "There is no available gateway" for the failure reason, but under the gateway connection menu there is a message stating "You don't need a gateway for this dataset, because all of its data sources are in the cloud, but you can use a gateway for enhanced control over how you connect."

The only difference between the two databases is that I'm accessing the first one through "OAuth2" authenication and the second one through "Basic" authentication. There didn't seem to be any issues when I was working with the data on Power BI desktop, but now it doesn't want to refresh. Has anyone run into this problem before? I'm not sure where to go because of the conflicting messages.