Fix FloatBar DPI-aware content sizing

[klken88]

Summary

Describe what changed and why.

Related issue

Fixes #

Affected areas

Check every area this PR changes or could affect:

• Tray panel
• Settings UI
• Config file / settings persistence
• CLI
• Provider-specific behavior
• Installer / release packaging
• Startup / background behavior
• Documentation
• Other:

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UI / tray proof

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Notes for reviewers

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[Finesssee]

Thanks for the PR, I will review this.

[Finesssee]

Thermo-nuclear code-quality review (automated; @Finesssee for merge gating)

Verdict: Approve on code quality (minor nits). Block on process before merge — see the last section.

The change is small, direct, and behaviorally correct. Switching set_size from LogicalSize to PhysicalSize and multiplying the measured CSS px by devicePixelRatio in FloatBar.tsx is the right model for per-monitor DPI: the native window ends up exactly content-sized in physical pixels, and flex: none keeps the content from re-expanding to fill it. The DPI-1.5 test (rect 100×20 + padding 8 → 162×42 physical) exercises the new path and would fail under the old LogicalSize code. No new abstraction, no file-size concern, no scattered special-casing.

Nits (non-blocking):

• window.rs: width.ceil().clamp(1.0, u32::MAX as f64) as u32 — the ceil() is redundant; FloatBar.tsx already sends Math.ceil(...). The lower clamp to 1.0 is the meaningful part (prevents a 0-size window); the u32::MAX upper clamp is belt-and-suspenders since f64 as u32 already saturates. Fine to keep as boundary defense — just noting it.
• FloatBar.tsx: the new window.addEventListener("resize", resizeToContent) fires on any webview resize, not only DPI changes. The existing lastResizeRef ±1 dedup guard breaks the self-feedback loop (set_size → resize event → re-measure → same px → early return), so it's safe; the listener is just slightly broader than its stated purpose. No change needed.
• No simpler reframing is visible — keeping LogicalSize and not multiplying would reintroduce the bug under WebView2 per-monitor scaling.

Process (required before merge per AGENTS.md):

• PR body is the unfilled template ("Describe what changed and why" / "Fixes #" blank, validation checkboxes unchecked). Please fill it in.
• This is a visual/DPI change. AGENTS.md requires CUA Driver proof after a fresh rebuild for UI/tray/float-bar PRs; none is attached. Please attach before/after screenshots at ≥1.0 and 1.5 scale (or state why CUA couldn't run + attach manual proof).
• Confirm the float-bar window still pins theme(Some(Dark)) and other webviews don't flip under auto after the PhysicalSize change (the known shared-process-profile hazard noted in AGENTS.md).

[Finesssee]

Merged 🎉 Thank you @klken88 — clean fix. CUA-verified on a real desktop debug build (scale 1.0): the float bar renders at full size, sits at its content rect, and toggles cleanly (proof-245 artifacts: settings-menu.png, floatbar-window.png). Note for the record: the shipped math (CSS px × devicePixelRatio → PhysicalSize) is also covered by your jsdom test at 1.5 scale; a live 1.5-scale run needs a scaled monitor, but the 1.0 non-regression plus the unit test cover the change. Ships in the next release.