[base-ui][docs] Remove redundant "Styled" prefix

[oliviertassinari]

A continuation of #37029. This feels much better. Open https://mui.com/base-ui/react-autocomplete/#hook, I can't imagine developers would want to use "Styled" in their actual implementation.

• If developers use the hooks, by default, every component present in the file is styled, so "styled" is noise.
• If they use the unstyled component, I think they should rename them all to be suffixed with Base.
  const Button = styled(ButtonBase)({}) makes a lot more sense to me than the opposite. The button comes first, then it's nature. I think it's easier to read when the component is first.
  So in https://mui.com/base-ui/react-button/#component, I think that we should rename the alias as well, the same way Radix suffix them with Primitive https://github.com/radix-ui/themes/blob/300260e3c3ed5fc491129b192760aad6f96c38ac/packages/radix-ui-themes/src/components/slider.tsx#L5.

Preview: https://deploy-preview-40478--material-ui.netlify.app/base-ui/react-autocomplete/#hook

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[danilo-leal]

Looks good! This is the type of thing that deserves internal documentation. In case this ever comes up again, we can share this as a guideline we follow instead of it being "silently" defined just by the code 👍

[oliviertassinari]

documentation

Agree, I think that we should agree on one of the components page as the gold standard and have these types of PRs to update it, so that when we review PRs, we can compare again the gold standard (feels better than a Notion page).

@samuelsycamore which component page should it be?

[oliviertassinari]

Adding @colmtuite to the loop as it's related to the docs experience for the demos of Base UI.

[colmtuite]

I agree on all changes. I have an open PR #40742 which focuses just on improving the functional CSS for the button demo. I'm planning to get back to that PR this afternoon.

Once that is merged, I'm planning to open another PR on the Button component to address imports/aliases and how to handle theme values and theming. We could then review that and potentially use it as a guide for updating other component docs.