Fix side menu to collapse until Chirpy hover or panel use

2 — Summary

The extension's in-page side menu on LinkedIn is permanently expanded, cluttering the page. It should stay collapsed to the Chirpy icon and expand only on hover or active use.

3 — Problem Statement

Users browsing LinkedIn with the SurroundR extension see the full vertical navbar menu (home, contacts, tasks, video, rewards, etc.) sticking out at all times, overlapping LinkedIn's own UI and drawing attention even when not in use. A user reported this via Featurebase ("make the side icon smaller"), and it reproduces on the LinkedIn feed. Impact not yet quantified, but it degrades the on-page experience for every extension user on every LinkedIn page.

4 — 🚦 Definition of Ready (Checklist)

Before entering a cycle, confirm:

• [ ] Problem statement is clear
• [ ] Acceptance criteria are defined
• [ ] Scope & non-goals are explicit
• [ ] Linked to relevant context
• [ ] Can be completed by one person in one sprint

If any box is unchecked → do not pull into sprint

5 — Acceptance Criteria

• [ ] Given a LinkedIn page with the extension active, when the user is not interacting with the side panel, then only the Chirpy icon is visible and all other menu icons are hidden
• [ ] Given the collapsed state, when the user hovers over the Chirpy icon, then the full side menu expands
• [ ] Given the expanded state, when the mouse pointer is over any part of the side panel, then the menu remains expanded
• [ ] Given the expanded state, when the mouse leaves both the Chirpy icon and the side panel, then the menu collapses immediately (no delay)
• [ ] Given any LinkedIn page type (feed, profile, company, Sales Navigator), when the page loads, then the menu initializes in the collapsed state
• [ ] Expand/collapse causes no layout shift or flicker in the underlying LinkedIn page

If this checklist is complete, the issue is done.

6 — Scope

In Scope

• Hover-to-expand / leave-to-collapse behavior for the in-page side menu
• Collapsed default state showing only the Chirpy icon
• Applies across all LinkedIn surfaces where the menu is injected

Out of Scope

• Resizing or restyling the individual menu icons themselves
• Chirpy asset consolidation (tracked in SUR-164)
• Changes to menu item contents, ordering, or destinations
• Onboarding focus mode behavior (SUR-126)

7 — Context & Links

| Type | Link / Reference | | -- | -- | | Featurebase (user feedback) | https://feedback.surroundr.io/p/make-the-side-icon-smaller | | Granola (call notes) | N/A | | PRD / Project | Extension 3.0 | | Incident | N/A | | Design | extension-3_7.html — github.com/SurroundR/wireframes (main) | | Technical Decision Record | N/A |

8 — Implementation Notes

• shadcn/ui + Tailwind; no custom CSS approaches
• Collapse on mouse-leave is immediate — no timeout/delay logic
• Screenshot of the always-expanded state on the LinkedIn feed must be attached manually in the Linear UI (programmatic upload is blocked)

9 — ✅ Definition of Done (Reference)

This issue is done when:

• [ ] Acceptance criteria are met
• [ ] Code is reviewed & merged
• [ ] Tests pass (functional + design where applicable)
• [ ] Feature is deployed
• [ ] Docs / release notes updated if needed