refactor(budget): 예산 추가/수정 모달 → 인라인 페이지 + 분류 바텀시트

- AppModal 제거, 목록/폼 v-if·v-else 전환(헤더·하단바 유지 + 뒤로가기)
- ?budget 라우트 바인딩으로 뒤로가기 시 닫힘
- 분류 선택은 트리거 → 바텀시트(CategoryPicker)

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/views/account/BudgetView.vue

@@ -1,12 +1,15 @@
 <script setup>
-import { computed, onMounted, reactive, ref } from 'vue'
+import { computed, onMounted, reactive, ref, watch } from 'vue'
+import { useRoute, useRouter } from 'vue-router'
 import { accountApi } from '@/api/accountApi'
 import { useDialog } from '@/composables/dialog'
 import IconBtn from '@/components/ui/IconBtn.vue'
-import AppModal from '@/components/ui/AppModal.vue'
 import CategoryPicker from '@/components/ui/CategoryPicker.vue'
+import BottomSheet from '@/components/ui/BottomSheet.vue'
 
 const dialog = useDialog()
+const route = useRoute()
+const router = useRouter()
 
 const now = new Date()
 const year = ref(now.getFullYear())
@@ -17,7 +20,18 @@ const budgetsRaw = ref([])
 const loading = ref(false)
 const error = ref(null)
 
+// 폼 — 라우트(?budget) 바인딩으로 뒤로가기 시 닫힘(페이지 전환처럼)
 const formOpen = ref(false)
+function openForm() {
+  formOpen.value = true
+  if (route.query.budget == null) router.push({ query: { ...route.query, budget: '1' } })
+}
+function closeForm() {
+  formOpen.value = false
+  if (route.query.budget != null) router.back()
+}
+watch(() => route.query.budget, (v) => { if (v == null) formOpen.value = false })
+
 const editId = ref(null)
 const form = reactive({
   category: '',
@@ -25,6 +39,9 @@ const form = reactive({
 })
 const submitting = ref(false)
 const formError = ref(null)
+// 분류 선택 바텀시트 — 최종 분류 정해지면 닫힘
+const catSheet = ref(false)
+watch(() => form.category, (v) => { if (v) catSheet.value = false })
 
 // 분류(지출) 드롭다운
 const categories = ref([])
@@ -152,7 +169,7 @@ function openCreate() {
   editId.value = null
   Object.assign(form, { category: '', monthly: null })
   formError.value = null
-  formOpen.value = true
+  openForm()
 }
 function openEdit(s) {
   const b = budgetsRaw.value.find((x) => x.id === s.id)
@@ -160,7 +177,7 @@ function openEdit(s) {
   editId.value = b.id
   Object.assign(form, { category: b.category, monthly: b.monthly })
   formError.value = null
-  formOpen.value = true
+  openForm()
 }
 
 async function submit() {
@@ -185,7 +202,7 @@ async function submit() {
   try {
     if (editId.value) await accountApi.updateBudget(editId.value, payload)
     else await accountApi.createBudget(payload, { year: year.value, month: month.value })
-    formOpen.value = false
+    closeForm()
     await load()
   } catch (e) {
     formError.value = e.response?.data?.message || '저장에 실패했습니다.'
@@ -213,6 +230,7 @@ onMounted(() => {
 
 <template>
   <section class="budget">
+    <template v-if="!formOpen">
     <div class="month-nav">
       <span class="mn-spacer"></span>
       <IconBtn icon="chevronLeft" title="이전 달" size="sm" @click="prevMonth" />
@@ -279,12 +297,26 @@ onMounted(() => {
       </li>
     </ul>
     <p v-else-if="!loading" class="msg">설정된 예산이 없습니다. "예산 추가"로 시작하세요.</p>
+    </template>
 
-    <!-- 추가/수정 모달 (월별) -->
-    <AppModal v-model="formOpen" :title="`예산 ${editId ? '수정' : '추가'}`">
+    <!-- 예산 추가/수정 (인라인 페이지 — 헤더·하단바 유지, 뒤로가기로 닫힘) -->
+    <div v-else class="budget-page">
+      <header class="ep-head">
+        <IconBtn icon="back" title="뒤로" @click="closeForm()" />
+        <span class="ep-title">예산 {{ editId ? '수정' : '추가' }}</span>
+      </header>
       <form class="budget-form" @submit.prevent="submit">
         <div class="field">
           <span class="field-label">카테고리</span>
+          <button
+            type="button" class="sheet-trigger" :class="{ empty: !form.category }"
+            :disabled="submitting" @click="catSheet = true"
+          >
+            <span class="st-label">{{ form.category || '분류를 선택하세요' }}</span>
+            <span class="st-caret">▾</span>
+          </button>
+        </div>
+        <BottomSheet v-model="catSheet" title="분류 선택">
           <CategoryPicker
             v-model="form.category"
             type="EXPENSE"
@@ -292,7 +324,7 @@ onMounted(() => {
             :disabled="submitting"
             @category-added="loadCategories"
           />
-        </div>
+        </BottomSheet>
 
         <label>월 예산<input v-model.number="form.monthly" type="number" min="0" placeholder="원" :disabled="submitting" /></label>
         <p class="note">설정한 월 예산 기준으로 이번 달 지출과 비교됩니다.</p>
@@ -300,11 +332,11 @@ onMounted(() => {
         <p v-if="formError" class="msg error">{{ formError }}</p>
 
         <div class="buttons">
-          <IconBtn icon="close" title="취소" @click="formOpen = false" />
+          <IconBtn icon="close" title="취소" @click="closeForm()" />
           <IconBtn icon="save" :title="editId ? '수정' : '등록'" variant="primary" type="submit" :disabled="submitting" />
         </div>
       </form>
-    </AppModal>
+    </div>
   </section>
 </template>
 
@@ -313,6 +345,52 @@ onMounted(() => {
   max-width: 640px;
   margin: 0 auto;
 }
+.budget-page .budget-form {
+  max-width: 460px;
+  margin: 0 auto;
+}
+.ep-head {
+  display: flex;
+  align-items: center;
+  gap: 0.5rem;
+  margin-bottom: 1.2rem;
+}
+.ep-title {
+  font-size: 1.2rem;
+  font-weight: 700;
+}
+.sheet-trigger {
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+  gap: 0.5rem;
+  width: 100%;
+  padding: 0.55rem 0.75rem;
+  border: 1px solid var(--color-border);
+  border-radius: 6px;
+  background: var(--color-background-soft);
+  color: var(--color-text);
+  font-size: 0.9rem;
+  cursor: pointer;
+  text-align: left;
+}
+.sheet-trigger:disabled {
+  opacity: 0.5;
+  cursor: not-allowed;
+}
+.sheet-trigger.empty .st-label {
+  opacity: 0.5;
+}
+.st-label {
+  overflow: hidden;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+}
+.st-caret {
+  opacity: 0.5;
+  font-size: 0.8rem;
+  flex-shrink: 0;
+}
 .head {
   display: flex;
   align-items: center;