UI/UX polish: fix doc type capitalization, sidebar tree depth cues, homepage doc-title tree

- Doc page: capitalize doc type (Documentation not documentation)
- Sidebar: tree-style with border-l per depth level, section separators
- Homepage: use doc titles from DB for tree nodes (not path segments)
- CustomFieldBadges: body field excluded from badges (added to STANDARD_KEYS)
- All section config centralized in packages/config/src/sections.ts

apps/web/app/[section]/[...slug]/page.tsx

@@ -390,8 +390,8 @@ export default async function DocPage({ params, searchParams }: DocPageProps) {
                   <span className="uppercase">{sectionInfo.label}</span>
                 </span>
                 <span className="text-xs text-[var(--text-dim)]">·</span>
-                <span className="text-xs text-[var(--text-muted)] capitalize">
-                  {doc.type}
+                <span className="text-xs text-[var(--text-muted)]">
+                  {doc.type.charAt(0).toUpperCase() + doc.type.slice(1)}
                 </span>
                 <span className="text-xs text-[var(--text-dim)]">·</span>
                 <span className="text-xs text-[var(--text-muted)] font-mono">