JetBrains: Add “New version” notification

Created by: vdavid

Fixes https://github.com/sourcegraph/sourcegraph/issues/38574

I've:

• Added the new notification
• Made sure the "set your access token" CTA is not displayed together with the update news
• Organized our notifications to categories

This is how it looks on Mac:

Caveats:

• We don't know the URL of our future blog post, so I'm currently using the plugin page URL for the "What's new" link.
• The icon is to the left of the action text rather than the right, which is not ideal, but I found no way to add it to its right.

Test plan

2-min Loom

App preview:

• Web
• Storybook

Check out the client app preview documentation to learn more.