refactor: use Nuxt 4 directory structure

utils/prompt.ts

@@ -1,14 +0,0 @@
-import type { ResearchFeedbackResult } from '~/components/ResearchFeedback.vue'
-import type { ResearchInputData } from '~/components/ResearchForm.vue'
-
-export function getCombinedQuery(
-  form: ResearchInputData,
-  feedback: ResearchFeedbackResult[],
-) {
-  return `Initial Query: ${form.query}
-Follow-up Questions and Answers:
-${feedback
-  .map((qa) => `Q: ${qa.assistantQuestion}\nA: ${qa.userAnswer}`)
-  .join('\n')}
-  `
-}

utils/tree-node.ts

@@ -1,28 +0,0 @@
-export function isChildNode(parentId: string, childId: string) {
-  return childId.length > parentId.length && childId.startsWith(parentId)
-}
-
-export function isParentNode(parentId: string, childId: string) {
-  return childId.length < parentId.length && childId.startsWith(parentId)
-}
-
-export function isRootNode(nodeId: string) {
-  return nodeId === '0' // equal to `nodeDepth(nodeId) === 1`
-}
-
-export function parentNodeId(nodeId: string) {
-  return nodeId.split('-').shift()
-}
-
-export function nodeIndex(nodeId: string) {
-  return parseInt(nodeId.split('-').pop()!)
-}
-
-export function nodeDepth(nodeId: string) {
-  return nodeId.split('-').length
-}
-
-/** Returns the next search breadth at a given node */
-export function searchBreadth(initialBreadth: number, nodeId: string) {
-  return Math.ceil(initialBreadth / Math.pow(2, nodeDepth(nodeId) - 1))
-}