fix(design): P0 buyer-blockers (FAB safe-gutter, mobile header, wire Brain follow-up)

[build-with-dhiraj]

Resolves the four P0 buyer-blockers from the LabOS design council report, plus the closely related P1-1 (same corner-overlay class). Scope is exactly the council's PR A + PR B + PR C, in one PR.

Files: Sidebar.tsx, BrainFlow.tsx, Landing.tsx, TopNav.tsx, LabSwitcher.tsx. src/lib/labs/mcclean.ts untouched. Zero em-dashes. Design system, hero headline, abstain/safety answers, and "Same primitives, stricter policy" all preserved.

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P0-1 + P1-1 — corner-overlay safe-gutter

Problem: the fixed bottom-left accessibility FAB occluded the sidebar live lab-status card (hiding the bus-factor-1 count) on all four flows; the bottom-right "prototype" tag overlapped the Brain send button.
Fix: reserve a pb-24 safe gutter at the foot of the sidebar so the FAB's ~88px strike zone can never sit on the status card; lift the Brain composer with pb-16 so the tag clears the send button.
Verified (1280px, both labs, all four flows): FAB-to-card clearance 27px on setup/journey/matrix/brain for McClean and Okafor; fabIntersectsCard: false everywhere; bus-factor value visible. On Brain, the prototype tag clears the send button by 27px (tagIntersectsSendBtn: false).

P0-2 — hero clips at 380px

Problem: the hero grid track resolved to a fixed width inside a 380px viewport, clipping the headline + CTA (the blue payoff clause) under the section's overflow-x: hidden.
Fix: grid-cols-1 below lg, minmax(0,...) on the lg two-column track, and min-w-0 on both grid children so the 1fr track shrinks below intrinsic content width.
Verified (380px, both labs): full H1 renders with no clipped glyph; all CTAs within the viewport; zero horizontal overflow (scrollWidth == 380).

P0-3 — lab switcher missing on mobile

Problem: the lab switcher was hidden md:flex, so the core McClean→Okafor demo was unreachable on a phone.
Fix: a compact avatar-only LabSwitcher variant in the mobile header (flex md:hidden); tightened the mobile header (smaller logo below sm, gaps, CTA padding) so it fits. Desktop treatment unchanged (full switcher display:flex, compact display:none).
Verified (380px): switcher is present and in-viewport on the landing page and flow pages; opening it and selecting Okafor switches the whole app (?lab=okafor, graph chrome → "Okafor Lab Knowledge Graph") with no page freeze (LBX-01 scroll-lock fix held); zero header overflow.

P0-4 + P1-4 — dead Brain follow-up

Problem: the follow-up button's onClick was () => {} — the click that proves "an honest gap becomes a routed action" did nothing, and no live affordance remained after the first answer.
Fix: wired onClick to append a variant-aware routed confirmation row (capture vs escalation), derived from the clicked follow-up's own copy so it works for either lab without touching the per-lab scripts; the follow-up is consumed (no double-fire); suggested questions + input stay live.
Verified (both labs): clicking "Capture this gap, route to the PI" (McClean abstain) renders a green Routed card: "Logged as an open knowledge gap and added to the capture queue…"; clicking "Escalate to Dr. Ada Okafor" (Okafor safety) renders "Owner notified. They will confirm the verified step before you proceed…". Four suggested-question chips + enabled input remain after each answer.

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CI status

• tsc --noEmit: clean (exit 0)
• next build: clean (9/9 static pages, lint + types passed)
• Browser console: 0 errors across the whole verification session

Before/after screenshots captured during verification (mobile landing at 380px, mobile switcher open, Brain abstain before/after follow-up, desktop landing).

Do not merge, do not deploy — for review only. A production deploy is live on this repo's main checkout.

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