[docs] Improve access to the API docs from the demo pages

Motivation

This proposal is all about the speed of navigation. What would make traversing through the docs easier? Besides improving the search experience, which we did a few months ago, merging the demo page with the component API page sounds like a good idea in this direction. For me, personally, having them separated breaks my navigation flow a bit. Additionally, the Component API folder on the side nav is sorted alphabetically whereas the Component folder is not (sorted through a specific order), which frequently gets me confused.

I also think that having everything under the same "umbrella" would facilitate learning components that are made out of several smaller ones — Text Field might be the most illustrative of this.

How this could look

Here's the first design to kick this off.

Down sides

Is there any we should consider and bring to light? What would we lose or run the risk of making worse if we moved forward with this? I can't see anything right now. I remember we talked about that not even from an SEO standpoint this would be bad. So, what else?

Related issue

The look & feel of the API table: #34085.

cc @mui/maintainers

Start by reviewing the demo pages, the Component API folder, and the side-nav ordering described in the issue, then compare the related API-table issue #34085. The proposal needs a maintainer decision on the information architecture and a concrete definition of what merging or regrouping the pages would mean before completion can be judged.