[docs-infra] Rename package to @mui/internal-api-docs-builder

[brijeshb42]

and make it public to be published and used in X docs.

Also migrate other code accordingly to use the new package name.

• I have followed (at least) the PR section of the contributing guide.

[mui-bot]

	Fails
🚫	Danger failed to run dangerfile.js.

Error Error

Cannot find module '@mui/internal-docs-utils'
Require stack:
- /tmp/material-ui/packages-internal/api-docs-builder/src/buildApiUtils.ts?namespace=1776165293050
- /tmp/material-ui/packages-internal/api-docs-builder/src/buildApi.ts?namespace=1776165293050
- /tmp/material-ui/packages-internal/api-docs-builder/src/index.ts?namespace=1776165293050
- /tmp/material-ui/scripts/dangerFileContent.ts?namespace=1776165293050
- /tmp/material-ui/node_modules/.pnpm/tsx@4.21.0/node_modules/tsx/dist/get-pipe-path-BoR10qr8.cjs
- /tmp/material-ui/node_modules/.pnpm/tsx@4.21.0/node_modules/tsx/dist/cjs/api/index.cjs
- dangerfile.js
- /tmp/material-ui/node_modules/.pnpm/danger@13.0.7_encoding@0.1.13/node_modules/danger/distribution/runner/runners/inline.js
- /tmp/material-ui/node_modules/.pnpm/danger@13.0.7_encoding@0.1.13/node_modules/danger/distribution/commands/danger-runner.js
Error: Cannot find module '@mui/internal-docs-utils'
Require stack:
- /tmp/material-ui/packages-internal/api-docs-builder/src/buildApiUtils.ts?namespace=1776165293050
- /tmp/material-ui/packages-internal/api-docs-builder/src/buildApi.ts?namespace=1776165293050
- /tmp/material-ui/packages-internal/api-docs-builder/src/index.ts?namespace=1776165293050
- /tmp/material-ui/scripts/dangerFileContent.ts?namespace=1776165293050
- /tmp/material-ui/node_modules/.pnpm/tsx@4.21.0/node_modules/tsx/dist/get-pipe-path-BoR10qr8.cjs
- /tmp/material-ui/node_modules/.pnpm/tsx@4.21.0/node_modules/tsx/dist/cjs/api/index.cjs
- dangerfile.js
- /tmp/material-ui/node_modules/.pnpm/danger@13.0.7_encoding@0.1.13/node_modules/danger/distribution/runner/runners/inline.js
- /tmp/material-ui/node_modules/.pnpm/danger@13.0.7_encoding@0.1.13/node_modules/danger/distribution/commands/danger-runner.js
    at node:internal/modules/cjs/loader:1365:15
    at nextResolveSimple (/tmp/material-ui/node_modules/.pnpm/tsx@4.21.0/node_modules/tsx/dist/register-D46fvsV_.cjs:4:1004)
    at /tmp/material-ui/node_modules/.pnpm/tsx@4.21.0/node_modules/tsx/dist/register-D46fvsV_.cjs:3:2630
    at /tmp/material-ui/node_modules/.pnpm/tsx@4.21.0/node_modules/tsx/dist/register-D46fvsV_.cjs:3:1542
    at resolveTsPaths (/tmp/material-ui/node_modules/.pnpm/tsx@4.21.0/node_modules/tsx/dist/register-D46fvsV_.cjs:4:760)
    at Function._resolveFilename (/tmp/material-ui/node_modules/.pnpm/tsx@4.21.0/node_modules/tsx/dist/register-D46fvsV_.cjs:4:1102)
    at defaultResolveImpl (node:internal/modules/cjs/loader:1021:19)
    at resolveForCJSWithHooks (node:internal/modules/cjs/loader:1026:22)
    at Function.<anonymous> (node:internal/modules/cjs/loader:1175:37)
    at _module2.default._load (/tmp/material-ui/node_modules/.pnpm/override-require@1.1.1/node_modules/override-require/dist/overrideRequire.js:43:25)

Dangerfile

-------------------^

Generated by 🚫 dangerJS against 9d55419

[code-infra-dashboard]

Bundle size

Bundle	Parsed size	Gzip size
@mui/material	0B(0.00%)	0B(0.00%)
@mui/lab	0B(0.00%)	0B(0.00%)
@mui/private-theming	0B(0.00%)	0B(0.00%)
@mui/system	0B(0.00%)	0B(0.00%)
@mui/utils	0B(0.00%)	0B(0.00%)

Details of bundle changes

Deploy preview

https://deploy-preview-48230--material-ui.netlify.app/

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