Add section grouping to shared note tabs

Notes can now be clustered into named sections in the tab bar: each tab
gets a 🏷 button to assign it to a section, and clicking a section's
label renames (or, given an empty name, ungroups) every page in it.

note_pages gains a `section` column. Since the app has no migration
framework, database.py adds the column to existing SQLite files at
startup via PRAGMA table_info + ALTER TABLE. core/notes.set_section()
keeps same-section pages contiguous by renumbering position whenever a
page's section changes, so the tab bar and the AI-facing title list
(now grouped under "## section" headings) can both treat "adjacent" as
"same group" without a separate ordering field.

Also fixes a bug in the tab rename input: ref="renameInput" sits inside
a nested v-for, which Vue 3 binds as an array rather than a single
element, so renameInput.value?.select() was throwing on every rename.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

backend/app/db/models.py

@@ -115,7 +115,8 @@ class NotePage(Base):
     id: Mapped[int] = mapped_column(Integer, primary_key=True, autoincrement=True)
     title: Mapped[str] = mapped_column(String)
     content: Mapped[str] = mapped_column(Text, default="")
-    position: Mapped[int] = mapped_column(Integer, default=0)  # タブの並び順
+    position: Mapped[int] = mapped_column(Integer, default=0)  # タブの並び順（セクションでまとめる際、同じセクションのページは連続させる）
+    section: Mapped[str | None] = mapped_column(String, nullable=True)  # タブをグループ化するセクション名。未設定なら未分類
     created_at: Mapped[datetime] = mapped_column(DateTime, default=lambda: datetime.now(timezone.utc))
     updated_at: Mapped[datetime] = mapped_column(DateTime, default=lambda: datetime.now(timezone.utc), onupdate=lambda: datetime.now(timezone.utc))