Please look at the last part of your url:
bbox=12550042.800086519,-802894.5451074906,12550348.548199661,-802588.7969943506
These are not geographic coordinates.

You have two ways:
1. Configure your server to work with coordinates.
2. Find a way to convert the coordinates from the map to these values.

Based on the documentation and examples I have seen in Atlas Example (Custom WMS Provider), the custom WMS provider URL uses EPSG:4326 (Latitude/Longitude), but I would like to use EPSG:3857 for the coordinates in the WMS URL.
Here is a brief description of the problem I am facing:

WMS URL Requirements:
The URL I am using for the WMS server requires EPSG:3857 for the BBOX coordinates. The URL looks as follows:

http://localhost/cgi-bin/mapserv.exe?map=C%3A%2Fms4w%2Fapps%2Fcgi-viewer%2Fmap%2FSeaChart_DAY_BRIGHT.map&&service=WMS&request=GetMap&layers=General&styles=&format=image%2Fpng&transparent=true&version=1.1.1&srs=EPSG%3A3857&width=256&height=256&bbox=12550042.800086519,-802894.5451074906,12550348.548199661,-802588.7969943506

Issue Encountered:

When the map is loaded, the screen turns black, and a question mark icon appears on the screen, indicating that the map is not loading correctly. I have verified that the WMS URL used follows the correct format with EPSG:3857.