The Web. The Contents function can lead to credential issues for Power BI when connecting to web-based data sources and APIs that require authentication. For example, Power BI's Privacy Levels can prevent connections between different data sources because a violation is considered a security risk. Fix this by navigating to File > Options and settings > Data source settings in Power BI Desktop and setting the Privacy Level of the data source to either Organizational or Public.
Another issue occurs when dynamic URLs are used within Web Content. Power BI expects a static URL for authentication, so unless your query expressly defines a simple URL syntactically (for example, with parameters or variables), authentication will completely disregard it as a valid data source. The proposed workaround is connecting using RelativePath and Query parameters together inside Web Contents while keeping the base URL static to allow Power BI to handle authentication.
If you're dealing with OAuth-based APIs, ensure you've done proper token handling with the Web. Contents header options. Sometimes, you'll need to re-authenticate in Power BI Service (after publishing) to revalidate credentials. If the issue persists, please share more details about the kind of API or external source you are connecting to.