First encounter with the site is confusing

### Describe the problem

It's your first time on docs.flutter.dev and you're new to Flutter. There are, in my view, way too many places calling for your attention, some, in duplicate fashion. There's also a lack of introduction to Flutter, you're just faced with a huge number of links, unclear where to go next.

The second issue is the Get started button links to different pages
- from https://docs.flutter.dev/ it links to https://docs.flutter.dev/learn/pathway
- from https://flutter.dev/blog it links to https://docs.flutter.dev/get-started/quick

### Expected fix

- Reduce clutter and duplicative entrypoints on docs.flutter.dev
- Make this page an intro page, show a bit of code, perhaps a Dartpad, then show some examples, and then then a limited (ideally 1) next step call to action
- Reduce sidebar and top-bar entrypoints to installing / getting started to a single one

#### Some inspo:

These all have similarities: overview, intro, examples, minimal get started / installation / learning path calls to actions

Start by comparing the current docs.flutter.dev homepage with the two Get started destinations named in the issue, then review the linked inspiration images. Define a consolidated introductory flow with fewer entrypoints; done means the homepage has a clear introduction, examples, and a consistent limited next step.

Written by the indexing model from the issue text.