Fix playground tab buttons

[tevanburen]

Description

Fixed the playground sidebar's tab-strip controls (maximize, open-inline, close) overlapping and misaligning with the tabs, and removed the "N more" overflow menu so tabs just scroll. Also tightened spacing between the mic and prompt-optimizer buttons in the room input toolbar.

Changes Made

• Moved sidebar controls into FlexLayout's native toolbar API instead of an absolutely-positioned overlay, fixing overlap and right-alignment
• Hid FlexLayout's overflow ("N more") button and centered the tab strip via the existing DOM-patching effect in room-sidebar.tsx
• Nudged spacing between the mic and prompt-optimizer buttons in room-input.tsx

How to Test

1. Open the sidebar with several tabs — controls should sit right-aligned and centered with the tabs, no overlap, no overflow menu, tabs just scroll
2. Check mic/prompt-optimizer spacing in the room input toolbar

[snyk-io]

✅ Snyk checks have passed. No issues have been found so far.

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✅	Open Source Security	0	0	0	0	0 issues

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