[types] PayloadChildRenderFunction isn't exported, so popup Root children types aren't portable #6203

Bug report

Current behavior

The children prop of the popup roots (Dialog.Root, Menu.Root, Popover.Root, Tooltip.Root, PreviewCard.Root, Drawer.Root) includes PayloadChildRenderFunction<Payload>. That type is declared in utils/popups/popupStoreUtils and isn't exported from any public entry point (./utils isn't in the package's exports map), so declaration emit can't name it:

import { Dialog } from '@base-ui/react/dialog';

export const children = (null as unknown as Dialog.Root.Props<string>)['children'];

error TS2883: The inferred type of 'children' cannot be named without a reference to
'PayloadChildRenderFunction' from './node_modules/@base-ui/react/utils/popups/popupStoreUtils.mjs'.
This is likely not portable. A type annotation is necessary.

We hit it while generating a standalone .d.ts that documents components wrapping these roots. Every other root prop resolves to a public type (for example handle is reachable as Dialog.Handle). children is the only one that points at an internal file.

Expected behavior

PayloadChildRenderFunction (or the children type as a whole) is exported publicly, so wrapper and documentation tooling can name it. That's the same treatment #2912 gave the other top-level types for #2881.

Reproducible example

tsconfig.json:

{
  "compilerOptions": {
    "declaration": true,
    "emitDeclarationOnly": true,
    "module": "ESNext",
    "moduleResolution": "bundler",
    "jsx": "react-jsx",
    "strict": true,
    "skipLibCheck": true
  },
  "files": ["index.ts"]
}

index.ts is the snippet above. Run tsc -p ..

Base UI version

1.9.0 (@base-ui/react)

Which browser are you using?

N/A (types only)

Which OS are you using?

N/A

Which assistive tech are you using (if applicable)?

N/A

Additional context

TypeScript 7.0.2.