Code Insights: Adopt separate insights loading system for the homepage and directory page.

Created by: vovakulikov

Requirements

Migration from the extension API should be resolved to be able to start this issue https://github.com/sourcegraph/sourcegraph/issues/23187

Context

Currently, we have 3 different places for insights in the main Sourcegraph app.

• Insight page (supports only search-based, code-stats, and BE insights)
• Homepage supports only search-based and BE insights
• Directory page supports all extension insights (search-based, code-stats, other insight extensions from the extension store like codecov) and BE insights

With the new loading system which this ticket implies https://github.com/sourcegraph/sourcegraph/issues/23187 we should adopt the new loading system for the homepage and directory page as well to be ably to support all types of insights (BE insights, search-based built-in, code-stats built-in let's call them FE insights, and extension based insights) at any place from the list above.

For that, we have to implement reusable logic or reusable components for the loading and viewing all these 3 types of insight in these places (BE insights, FE insights - built-in search and code stats insights, extension-based insights)