feat: add BranchMap sidebar with BranchNode tree visualization

BranchNode renders a branch button with depth-based indent, status icon,
and status badge using the design system color palette. BranchMap builds
a tree from the flat branch list via buildTree/flattenTree and renders
all nodes with a GitBranch header.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

frontend/src/components/session/BranchMap.tsx

@@ -0,0 +1,81 @@
+import { GitBranch } from 'lucide-react'
+import { BranchNode } from './BranchNode'
+import type { BranchResponse } from '@/types/branching'
+
+interface BranchTreeNode {
+  branch: BranchResponse
+  depth: number
+  children: BranchTreeNode[]
+}
+
+function buildTree(branches: BranchResponse[]): BranchTreeNode[] {
+  const map = new Map<string, BranchTreeNode>()
+  const roots: BranchTreeNode[] = []
+
+  // First pass: create nodes
+  for (const branch of branches) {
+    map.set(branch.id, { branch, depth: 0, children: [] })
+  }
+
+  // Second pass: assign parents / roots
+  for (const branch of branches) {
+    const node = map.get(branch.id)!
+    if (branch.parent_branch_id && map.has(branch.parent_branch_id)) {
+      const parent = map.get(branch.parent_branch_id)!
+      node.depth = parent.depth + 1
+      parent.children.push(node)
+    } else {
+      roots.push(node)
+    }
+  }
+
+  return roots
+}
+
+function flattenTree(nodes: BranchTreeNode[]): Array<{ branch: BranchResponse; depth: number }> {
+  const result: Array<{ branch: BranchResponse; depth: number }> = []
+  for (const node of nodes) {
+    result.push({ branch: node.branch, depth: node.depth })
+    if (node.children.length > 0) {
+      result.push(...flattenTree(node.children))
+    }
+  }
+  return result
+}
+
+interface BranchMapProps {
+  branches: BranchResponse[]
+  activeBranchId: string | null
+  onSelectBranch: (branchId: string) => void
+}
+
+export function BranchMap({ branches, activeBranchId, onSelectBranch }: BranchMapProps) {
+  const roots = buildTree(branches)
+  const flat = flattenTree(roots)
+
+  return (
+    <div className="flex flex-col gap-1">
+      <div className="flex items-center gap-1.5 px-2 pb-2">
+        <GitBranch size={14} className="text-muted" />
+        <span className="text-[10px] font-semibold uppercase tracking-wider text-muted">
+          Branch Map
+        </span>
+        <span className="ml-auto text-[10px] text-muted">{branches.length}</span>
+      </div>
+
+      {flat.length === 0 ? (
+        <p className="px-2 text-xs text-muted">No branches yet.</p>
+      ) : (
+        flat.map(({ branch, depth }) => (
+          <BranchNode
+            key={branch.id}
+            branch={branch}
+            depth={depth}
+            isActive={branch.id === activeBranchId}
+            onClick={onSelectBranch}
+          />
+        ))
+      )}
+    </div>
+  )
+}

frontend/src/components/session/BranchNode.tsx

@@ -0,0 +1,91 @@
+import { CircleDot, CheckCircle2, XCircle, Circle, RotateCcw } from 'lucide-react'
+import { cn } from '@/lib/utils'
+import type { BranchResponse } from '@/types/branching'
+
+type BranchStatus = BranchResponse['status']
+
+interface StatusConfig {
+  icon: React.ElementType
+  textClass: string
+  badgeClass: string
+  label: string
+}
+
+const STATUS_CONFIG: Record<BranchStatus, StatusConfig> = {
+  active: {
+    icon: CircleDot,
+    textClass: 'text-accent',
+    badgeClass: 'bg-accent-dim text-accent-text',
+    label: 'Active',
+  },
+  solved: {
+    icon: CheckCircle2,
+    textClass: 'text-[#34d399]',
+    badgeClass: 'bg-[rgba(52,211,153,0.10)] text-[#34d399]',
+    label: 'Solved',
+  },
+  dead_end: {
+    icon: XCircle,
+    textClass: 'text-[#f87171]',
+    badgeClass: 'bg-[rgba(248,113,113,0.10)] text-[#f87171]',
+    label: 'Dead End',
+  },
+  untried: {
+    icon: Circle,
+    textClass: 'text-muted',
+    badgeClass: 'bg-[rgba(79,86,102,0.20)] text-muted',
+    label: 'Untried',
+  },
+  revived: {
+    icon: RotateCcw,
+    textClass: 'text-[#eab308]',
+    badgeClass: 'bg-[rgba(234,179,8,0.10)] text-[#eab308]',
+    label: 'Revived',
+  },
+}
+
+interface BranchNodeProps {
+  branch: BranchResponse
+  depth: number
+  isActive: boolean
+  onClick: (branchId: string) => void
+}
+
+export function BranchNode({ branch, depth, isActive, onClick }: BranchNodeProps) {
+  const config = STATUS_CONFIG[branch.status]
+  const Icon = config.icon
+
+  return (
+    <button
+      type="button"
+      onClick={() => onClick(branch.id)}
+      style={{ paddingLeft: `${8 + depth * 16}px` }}
+      className={cn(
+        'w-full flex items-center gap-2 py-2 pr-3 text-left rounded-md transition-colors',
+        'hover:bg-elevated',
+        isActive && 'bg-accent-dim border-l-2 border-accent'
+      )}
+    >
+      <Icon
+        size={14}
+        className={cn('shrink-0', config.textClass)}
+      />
+      <span
+        className={cn(
+          'flex-1 text-sm truncate',
+          isActive ? 'text-heading font-medium' : 'text-primary'
+        )}
+      >
+        {branch.label}
+      </span>
+      <span
+        className={cn(
+          'text-[10px] font-semibold uppercase tracking-wider px-1.5 py-0.5 rounded-full shrink-0',
+          config.badgeClass
+        )}
+      >
+        {config.label}
+      </span>
+    </button>
+  )
+}