Well that would be quite expensive. I replicated that cost of 344,000~ credits by removing any processing extent restriction.
My bounding box layer was created in ArcGIS Pro and then published, but that should not cause that issue.
When using these tools in Map Viewer Classic, there are the Analysis Environments accessible from the cog icon in the top right of the analysis pane. This is where you can specify the processing extent using the polygon layer. Make sure this is set to your polygon layer. When you use the processing extent option, the "Use current map extent" will uncheck itself, because you changed how the "extent" is being defined.