Build a Project Management Tool in Lovable

Build a multi-tenant Kanban project management tool. Stack: React + Vite + TypeScript + Tailwind + shadcn/ui (already scaffolded), React Router, Supabase JS client against Lovable Cloud, dnd-kit for drag-and-drop.

## Database schema (create one migration)

Create these 5 tables and enable RLS on ALL of them:

1. `organizations` — id (uuid pk default gen_random_uuid()), name (text not null), slug (text unique not null), created_by (uuid references auth.users(id)), created_at (timestamptz default now()).

2. `members` — id (uuid pk default gen_random_uuid()), org_id (uuid not null references organizations(id) on delete cascade), user_id (uuid references auth.users(id) on delete cascade), role (text not null default 'member', check role in ('owner','admin','member','viewer')), invited_email (text, null once accepted), accepted_at (timestamptz), created_at (timestamptz default now()). UNIQUE(org_id, user_id).

3. `projects` — id (uuid pk default gen_random_uuid()), org_id (uuid not null references organizations(id)), name (text not null), description (text), status (text default 'active', check in ('active','archived')), created_by (uuid references auth.users(id)), created_at (timestamptz default now()).

4. `tasks` — id (uuid pk default gen_random_uuid()), project_id (uuid not null references projects(id)), title (text not null), description (text), assignee_id (uuid references auth.users(id)), status (text not null default 'todo', check in ('todo','in_progress','done')), priority (text check in ('low','medium','high','urgent')), due_at (timestamptz), position (double precision not null default 0), created_at (timestamptz default now()).

5. `comments` — id (uuid pk default gen_random_uuid()), task_id (uuid references tasks(id) on delete cascade), author_id (uuid references auth.users(id)), body (text not null), created_at (timestamptz default now()).

ALSO add at the end of the migration:
`ALTER PUBLICATION supabase_realtime ADD TABLE tasks;`

Create these two SECURITY DEFINER plpgsql functions (NEVER SQL-language — they get inlined and lose the security boundary):

```sql
CREATE OR REPLACE FUNCTION is_org_member(p_org_id uuid)
RETURNS boolean LANGUAGE plpgsql SECURITY DEFINER STABLE AS $$
BEGIN
  RETURN EXISTS (
    SELECT 1 FROM members
    WHERE org_id = p_org_id AND user_id = auth.uid()
  );
END;
$$;

CREATE OR REPLACE FUNCTION can_see_project(p_project_id uuid)
RETURNS boolean LANGUAGE plpgsql SECURITY DEFINER STABLE AS $$
BEGIN
  RETURN EXISTS (
    SELECT 1 FROM projects p
    JOIN members m ON m.org_id = p.org_id
    WHERE p.id = p_project_id AND m.user_id = auth.uid()
  );
END;
$$;
```

RLS policies (NEVER subquery members from a members policy — always go through the SECURITY DEFINER function):
- organizations SELECT: USING (is_org_member(id))
- members SELECT: USING (is_org_member(org_id))
- members INSERT: WITH CHECK (is_org_member(org_id)) — for accepting invites
- projects SELECT/INSERT/UPDATE: USING (is_org_member(org_id)) / WITH CHECK (is_org_member(org_id))
- tasks SELECT/INSERT/UPDATE/DELETE: USING (can_see_project(project_id)) / WITH CHECK (can_see_project(project_id))
- comments SELECT/INSERT: USING (can_see_project((SELECT project_id FROM tasks WHERE id = task_id)))

Also create a SECURITY DEFINER function `create_org(p_name text, p_slug text) RETURNS uuid` that inserts into organizations AND into members(owner) atomically — so /onboarding can call one RPC instead of two separate inserts that would race against the org policy.

## Layout

Create `src/layouts/AppLayout.tsx` — top bar with OrgSwitcher dropdown (reads members rows for current user, lists org names) + user menu; left sidebar with project list for current org + 'New project' button; main scrollable area.

Create `src/contexts/OrgContext.tsx` — stores current org_id + slug from the URL param `/org/:slug`, exposes useOrg() hook used by all queries.

Create `src/components/AuthGuard.tsx` — redirects to /login if no session.

Create `src/components/OrgGuard.tsx` — verifies is_org_member(org_id_from_slug), redirects to /onboarding if user is not a member of any org, or to the first available org.

## Pages and routes

Create these routes:
- `/login` — email+password + Google OAuth sign-in
- `/onboarding` — two cards: 'Create new organization' (calls create_org RPC) and 'Accept invite via token' (reads token from URL, verifies, updates members row)
- `/org/:slug` — org dashboard: project list grid + 'New project' button + recent activity
- `/org/:slug/project/:projectId` — Kanban board (todo / in_progress / done columns)
- `/org/:slug/project/:projectId/list` — list view with sort/filter
- `/org/:slug/team` — member list + 'Invite' button (opens InviteMemberDialog)
- `/org/:slug/settings` — org name, danger zone (delete org)

## Components

Create:
- `src/components/OrgSwitcher.tsx` — shadcn Select or DropdownMenu listing user's orgs
- `src/components/KanbanBoard.tsx` — dnd-kit DndContext with three DragOverlay columns (todo, in_progress, done). On drop: compute new position as midpoint between neighbors (`(prev.position + next.position) / 2`, or `prev.position + 1` at end). Call `supabase.from('tasks').update({status, position}).eq('id', taskId)` and await before clearing optimistic state.
- `src/components/TaskCard.tsx` — compact card (36px density): title + assignee avatar + due date chip + priority badge (gray low / blue medium / amber high / rose urgent)
- `src/components/TaskDetailDrawer.tsx` — shadcn Sheet (right, 560px). Full task form: title, description, assignee picker (list of org members), priority, due date, status. Comment list + new comment input below.
- `src/components/InviteMemberDialog.tsx` — email input + role selector. On submit, calls invite-member Edge Function (wired in follow-up #2).
- `src/hooks/useRealtimeTasks.ts` — subscribes to `postgres_changes` on tasks filtered by `project_id=eq.${projectId}`. On INSERT/UPDATE/DELETE, mutates TanStack Query cache.

## Styling

Light + dark mode via shadcn ThemeProvider. Primary color: violet-600. Status columns color-coded: gray (todo) / amber (in_progress) / emerald (done). Priority badges as above. 36px compact card density.

Generate the migration first (confirm it includes BOTH SECURITY DEFINER functions and the ALTER PUBLICATION line), then the context + guards, then the layout, then pages in order.