Integrate the new api_max plan ($100/mo, $130 credits) from mono into the
nova web app, mirroring mono's tier semantics.
- Tiers: insert api_max between pro and scale; resolves to Pro-tier for feature gates while displaying as "Max" (queries.ts, use-token-usage)
- Billing page: Max plan card ("Most Popular"), checkout/cancel/invoice wiring; advanced carousel page now 3-up (Max/Scale/Enterprise); Scale builds on Max
- Carousel auto-opens to the page holding the current plan (Max/Scale/ Enterprise users land on their own card instead of Free+Pro)
- Cancel: retention dialog listing what you lose + type-to-confirm "CANCEL"
- Cancel/resume state mirroring console: detect canceledAt-scheduled cancellation, show "Cancelling" pill + "Cancels on {date} · N days left", and a "Resume plan" (uncancel) action
- Replace the top-left logo menu with an org switcher (Switch brain): lists organizations with avatar monograms, brand-blue active row, and the active org name (sans "Organization") shown above the supermemory wordmark.
- Switching an org persists the active org and reloads so all data re-scopes.
- Show each org's plan badge in the switcher, reusing the account settings badge (extracted OrgPlanBadge + resolveOrgPlan to a shared component).
- Match the profile dropdown to the same design (rows, hover/focus, border).
- Remove the 'Be part of the next supermemory app' research CTA card.
- Add hideCount prop to SpaceSelector; hide the space count in chat input.
