[popups] Use popup-backed floating context

[michaldudak]

Summary

• Replace mirrored floating root stores with popup-backed floating context adapters across the migrated popup components.
• Keep the floating context in store context while deriving open, refs, IDs, and transition state from the popup store.
• Fix StoreInspector serialization for popup contexts with circular back-references.
• Fix modal initial-focus timing so outside content is not aria-hidden while the trigger still has focus.

Verification

• Manual Chrome pass on docs experiments for Menu, Popover, Dialog, Tooltip, and PreviewCard.
• pnpm test:jsdom FloatingFocusManager --no-watch
• pnpm test:chromium FloatingFocusManager --no-watch
• pnpm test:jsdom DialogPopup --no-watch
• pnpm test:jsdom StoreInspector --no-watch
• pnpm test:jsdom PopupFloatingRootContext --no-watch
• pnpm typescript
• targeted pnpm eslint

[pkg-pr-new]

• base-ui-tanstack-start

• vite-css-base-ui-example

  pnpm add https://pkg.pr.new/mui/base-ui/@base-ui/react@4973
  

  pnpm add https://pkg.pr.new/mui/base-ui/@base-ui/utils@4973
  

commit: 48be362

[code-infra-dashboard]

Bundle size

Bundle	Parsed size	Gzip size
@base-ui/react	🔺+4.07KB(+0.87%)	🔺+861B(+0.58%)

Details of bundle changes

Performance

Total duration: 1,222.29 ms -57.08 ms^(-4.5%) | Renders: 50 ⁽⁺⁰⁾ | Paint: 1,878.40 ms -42.17 ms^(-2.2%)

Test	Duration	Renders
Menu open (500 items)	92.13 ms 🔺+18.48 ms(+25.1%)	12 (+0)

11 tests within noise — details

---

Check out the code infra dashboard for more information about this PR.

[netlify]

✅ Deploy Preview for base-ui ready!

Built without sensitive environment variables

Name	Link
🔨 Latest commit	48be362
🔍 Latest deploy log	https://app.netlify.com/projects/base-ui/deploys/6a218d8463c03500083d8ac3
😎 Deploy Preview	https://deploy-preview-4973--base-ui.netlify.app
📱 Preview on mobile	Toggle QR Code... Use your smartphone camera to open QR code link.
🤖 Make changes	Run an agent on this branch

---

To edit notification comments on pull requests, go to your Netlify project configuration.