Sidebar mode: enable pushContent so the panel pushes content left

[blove]

Summary

• chat-sidebar already supports `[pushContent]`: when true and `open`, the lib applies `margin-right: 28rem` to its default content slot. Setting `[pushContent]="true"` in sidebar-mode now pushes the page background left of the panel rather than overlaying.
• Restructured sidebar-mode to project the `.sidebar-mode__background` div INTO chat-sidebar's default `` slot (was a sibling). Now the push margin actually applies to it.
• Background height switched from `height: 100%` to `min-height: calc(100dvh - var(--demo-toolbar-height, 51px))` so the area below the toolbar is filled exactly.
• Override `min-height: 0 !important` on `.chat-sidebar__content` to defeat the lib's `min-height: 100vh` (would push content 51px past viewport in our flex column under the top toolbar).

Demo-only change. No lib touched.

Test plan

• Local chrome-mcp: panel open → `data-push: "true"`, `data-open: "true"`, `.chat-sidebar__content` margin-right 448px (= 28rem), background bgRight 1352 ≈ panelLeft 1351 (content cleanly bounded), pageOverflow 0
• Canonical demo redeploys on demo.threadplane.ai

🤖 Generated with Claude Code

[vercel]

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Project	Deployment	Actions	Updated (UTC)
threadplane	Ready	Preview, Comment	May 19, 2026 4:11am