feat(fuse): implement mkdir and mv with persistence

Add mkdir and mv (rename) FUSE operations to the virtual filesystem:

- mkdir: Create directories that persist across remounts via SQLite
- mv: Move/rename files and directories with database persistence

Changes:
- Add directories table to schema for user-created empty dirs
- Add tree operations: mkdir, rename_file, rename_directory
- Add DB methods for path updates and directory CRUD
- Remove MountOption::RO to allow write syscalls
- Load stored virtual_path from DB instead of regenerating
- Restore user directories on mount from directories table
- Upsert files to DB during origin scan

POSIX compliant: mv fails with ENOENT if parent doesn't exist
(use mkdir first, shell handles -p flag and brace expansion)

docs/v2/features/mv.md

@@ -0,0 +1,94 @@
+**Date**: 2026-05-17
+**Status**: Shipped
+
+# Feature: Move/Rename (mv)
+
+## Overview
+
+MusicFS supports moving and renaming files and directories within the virtual filesystem. Moves are persisted to the SQLite database and survive remounts.
+
+## Behavior
+
+### File Rename
+
+```bash
+mv "/mnt/music/Artist/Album/old.flac" "/mnt/music/Artist/Album/new.flac"
+```
+
+- Renames file within same directory
+- Updates `virtual_path` in database
+- Original file on origin is unchanged
+
+### File Move
+
+```bash
+mv "/mnt/music/Artist/Album/track.flac" "/mnt/music/Other Artist/Other Album/track.flac"
+```
+
+- Moves file to different directory
+- **Requires target directory to exist** (use `mkdir` first)
+- Returns `ENOENT` if target parent doesn't exist
+
+### Directory Rename
+
+```bash
+mv "/mnt/music/Old Artist" "/mnt/music/New Artist"
+```
+
+- Renames directory and all descendants
+- All files under the directory have their `virtual_path` updated in DB
+- Single atomic operation
+
+### Directory Move
+
+```bash
+mv "/mnt/music/Artist/Album" "/mnt/music/Other Artist/Album"
+```
+
+- Moves directory subtree to new parent
+- **Requires target parent to exist**
+- Returns `ENOENT` if target parent doesn't exist
+
+## Error Codes
+
+| Condition | Error |
+|-----------|-------|
+| Source doesn't exist | `ENOENT` |
+| Target already exists | `EEXIST` |
+| Target parent doesn't exist | `ENOENT` |
+| Source is file but treated as dir | `EISDIR` |
+| Source is dir but treated as file | `ENOTDIR` |
+
+## Persistence
+
+- File moves: `virtual_path` column updated in `files` table
+- Directory moves: All matching `virtual_path` entries updated with new prefix
+- User directories: Tracked in separate `directories` table
+- Changes persist across unmount/remount cycles
+
+On mount, the CLI:
+1. Scans origin files
+2. For each file, checks DB for stored `virtual_path` (by origin_id + real_path)
+3. Uses stored path if found, otherwise generates from metadata
+4. Restores user-created directories from `directories` table
+
+## Limitations
+
+- **Read-only content**: File contents cannot be modified, only paths
+- **No cross-origin moves**: All files remain on their original origin
+- **No overwrite**: Moving to existing path fails (no implicit delete)
+
+## Implementation
+
+| Component | File |
+|-----------|------|
+| Database | `crates/musicfs-cache/src/db.rs` |
+| Tree | `crates/musicfs-cache/src/tree.rs` |
+| FUSE | `crates/musicfs-fuse/src/filesystem.rs` |
+
+### Key Functions
+
+- `Database::update_virtual_path()` - Update single file path
+- `Database::rename_directory()` - Bulk update paths with prefix
+- `VirtualTree::rename_file()` - Move file node in tree
+- `VirtualTree::rename_directory()` - Move directory subtree