Will VBAs Internet Control function after IE 11 end of life in Jun '22?

It won't magically disappear but it won't ever be updated again. It might also be absent from future versions of Windows, like you have noticed. If you rely on this code you will need to find a way to install IE on machines where it isn't installed. I would not want to be in that position. Running EOL libraries like this opens you up to potential security and reliability concerns. You want to have a plan B in the works before you suddenly need it.

The new web browser in Windows (Edge) is found in an object called Microsoft.Web.WebView2 or Windows.Web.Winmd which are not COM visible. There is an open question about that

If you make an office addin solution in VB.NET or C# then you can use this new WebView. You could make a command line tool that is called from Excel, and returns results to a file, like CSV.

Ultimately, you're better off using the right tool for the job. You can still process the data in Excel but the actual data collection should be done by a modern web scraper or a VBA library.