Web App Builds But Only Shows Default ASP.NET Page – Why?

Providing us an example of what you're seeing and what you expect would be useful here. We have no idea what you mean by ASP.NET Welcome screen. If you created a standard MVC web application then its index.html/default.html page contains some basic information. It is this HTML page that will be shown when the site runs. If you want different content then you need to update the default page to contain that content, change the default page (not recommend) that is loaded by the server, or redirect to the page you care about. Updating the default page is the standard/recommended approach.

You tagged this with ASP.NET API. If you're building a web API project then there is likely no UX (views) at all. In this case you can just add a default.html page to your site, under wwwroot if you're using ASP.NET Core, and the server will show it by default. This is commonly done to provide basic information about the API.

If you're using OpenAPI/Swagger for your API then you'd need to add the necessary middleware, assuming ASP.NET Core, to have it auto-generate the OpenAPI UX. Then you'd need to set your startup page to be the URL to the OpenAPI UX. This is generally done in the launchsettings.json file. For the actual site, when hosted on a web server, you'd want to add a redirect in your startup code.