Change Product badge on the homepage to be actual links

[hugocaillard]

I think that the product badges on the homepage should be links to relevant documentation pages.

(Especially since they look like buttons/links)

[ginny-d]

Here are the hover effect mockups: https://www.figma.com/design/WYxzBZubEGwbbzFq79eNim/Docs-Working-File?node-id=1005-728&t=d6dlfBDZ25TaHqPk-1

+ Adding to this:

• Replace the "+3 more" tag for the actual tools that are missing
• Fix the tag design so it looks like on Figma:
  
• Use the dark mode-adjusted images: