refactor(backend): split into api/ schemas/ services/ clients/ layers

4-phase restructuring of the previously flat backend/ package. Each
phase lands as a single squash commit so future bisects stay readable
per phase if needed.

## Phase 1 — move + shim (location-only, zero behavior change)
* git mv 14 files into api/ schemas/ services/ clients/ subpackages
  (history preserved via RM/R renames)
* New files: api/{admin,auth,dependencies,jupyter,platform,resources,
  scripts,storage}.py + api/schedules/{schedules,runs}.py
* New files: schemas/{auth,common,jupyter,platform,resources,
  schedules,scripts}.py
* New files: clients/{rclone,runtime,scheduler}.py
* Old paths kept as 1-line `from backend.<new> import *` shims so
  tests/main.py/importers kept working untouched
* schemas/__init__.py now re-exports from backend.schemas.<domain>

## Phase 2 — APIRouter prefix consolidation
* Every APIRouter() now carries its prefix (e.g. prefix="/api/v1/auth")
  and decorators are stripped of the redundant path prefix
* URL paths exposed to the frontend are byte-identical to before
* Affected: api/{auth,jupyter,admin,platform,resources,scripts,
  storage}.py + api/schedules/{schedules,runs}.py

## Phase 3 — first service-layer extraction
* backend.services.schedules.validate_dag moved out of api/
  (pure DAG validator, no Request/BackgroundTasks/DB)
* api/schedules/schedules.py now re-exports the symbol so existing
  4 callsites keep working unchanged
* Added backend/tests/test_validate_dag.py: 8 unit tests covering
  DAG_EMPTY, linear chain, diamond, cycle, self-edge, duplicate
  edge, orphan edge, multi-root ordering

## Phase 4 — delete shims + unify test imports
* Removed 14 flat shim files + schemas/__init__.py
* Migrated 5 test files (32 import sites) to new paths:
  backend.scripts.* → backend.api.scripts.*
  backend.resources.* → backend.api.resources.*
  backend.jupyter.* → backend.api.jupyter.*
  backend.runtime_client.* → backend.clients.runtime.*
  backend.schemas.UpdateScriptRequest → backend.schemas.scripts.*
* audit.py kept at backend.audit (main.py references it; not a
  shim, real code)

## Final structure
backend/src/backend/
  main.py, audit.py, __init__.py
  api/            (10 files: routes + 2 subpackage)
  schemas/        (7 files: Pydantic contracts)
  services/       (storage + schedules)
  clients/        (rclone, runtime, scheduler)

## Verification
* uv run python -m compileall backend/src backend/tests — clean
* uv run --package backend pytest backend/tests -q — 122 passed
  (114 → 114 → 122 → 122 across phases)
* grep -r 'from backend\.\(scripts\|resources\|...\)' backend/ — 0 hits
* git blame --follow still traces file origins through the renames

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

backend/tests/test_count_scripts.py

@@ -15,7 +15,7 @@ from unittest.mock import AsyncMock, MagicMock
 
 import pytest
 
-from backend.scripts import count_scripts
+from backend.api.scripts import count_scripts
 
 
 def _ctx(
@@ -139,7 +139,7 @@ async def test_count_scripts_route_declared_before_script_id_route() -> None:
     """Static check: the `/api/v1/scripts/count` route MUST be declared in
     scripts.py before `/api/v1/scripts/{script_id}/...`, otherwise FastAPI's
     declaration-order matching will interpret `count` as a script_id."""
-    from backend.scripts import count_scripts, get_script
+    from backend.api.scripts import count_scripts, get_script
 
     assert callable(count_scripts)
     assert callable(get_script)