feat: implement create new type feature

Core implementation:
- CreateTypeDialog: simple dialog with name field for creating new types
- handleCreateType in useNoteActions: creates Type documents in type/ folder
- Dynamic sidebar sections: custom types (Recipe, Book, etc.) appear as new
  sidebar sections after built-in ones, each with a + button for instances
- Updated CreateNoteDialog: accepts custom types, shows them with blue accent
- handleCreateNote now supports custom types (folder = lowercased type name)

Product decisions:
- The + on Types section opens CreateTypeDialog (not CreateNoteDialog)
- Custom type sections use FileText icon and blue accent color by default
- Section labels are pluralized (e.g., "Recipes", "Books")

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/components/CreateTypeDialog.tsx

@@ -0,0 +1,64 @@
+import { useState, useRef, useEffect } from 'react'
+import { Dialog, DialogContent, DialogHeader, DialogTitle, DialogFooter } from '@/components/ui/dialog'
+import { Button } from '@/components/ui/button'
+import { Input } from '@/components/ui/input'
+
+interface CreateTypeDialogProps {
+  open: boolean
+  onClose: () => void
+  onCreate: (name: string) => void
+}
+
+export function CreateTypeDialog({ open, onClose, onCreate }: CreateTypeDialogProps) {
+  const [name, setName] = useState('')
+  const inputRef = useRef<HTMLInputElement>(null)
+
+  useEffect(() => {
+    if (open) {
+      setName('')
+      setTimeout(() => inputRef.current?.focus(), 50)
+    }
+  }, [open])
+
+  const handleSubmit = (e: React.FormEvent) => {
+    e.preventDefault()
+    const trimmed = name.trim()
+    if (!trimmed) return
+    onCreate(trimmed)
+    onClose()
+  }
+
+  return (
+    <Dialog open={open} onOpenChange={(isOpen) => { if (!isOpen) onClose() }}>
+      <DialogContent showCloseButton={false} className="sm:max-w-[380px]">
+        <DialogHeader>
+          <DialogTitle>Create New Type</DialogTitle>
+        </DialogHeader>
+        <form onSubmit={handleSubmit} className="space-y-4">
+          <div className="space-y-1.5">
+            <label className="text-xs font-medium uppercase tracking-wide text-muted-foreground">
+              Type Name
+            </label>
+            <Input
+              ref={inputRef}
+              placeholder="e.g. Recipe, Book, Habit..."
+              value={name}
+              onChange={(e) => setName(e.target.value)}
+            />
+            <p className="text-xs text-muted-foreground">
+              Creates a type document. Its properties become defaults for new docs of this type.
+            </p>
+          </div>
+          <DialogFooter>
+            <Button type="button" variant="outline" onClick={onClose}>
+              Cancel
+            </Button>
+            <Button type="submit" disabled={!name.trim()}>
+              Create
+            </Button>
+          </DialogFooter>
+        </form>
+      </DialogContent>
+    </Dialog>
+  )
+}