chore: format the tree and clear ruff's findings

Applies ruff format, ruff check --fix and prettier, so CI can gate on all three.
The surviving unused imports were all re-exports in __init__.py, now covered by a
per-file ignore; the pdf.js viewer and the generated openapi types join the
vendored code that eslint and prettier already skip.

backend/pyproject.toml

@@ -38,6 +38,11 @@ dev = [
     "pytest-databases[postgres]>=0.15.0",
 ]
 
+[tool.ruff.lint.per-file-ignores]
+# The package __init__.py files exist to re-export their modules' public names, so every
+# import in them is "unused" as far as F401 is concerned.
+"__init__.py" = ["F401"]
+
 [tool.pytest.ini_options]
 asyncio_mode = "auto"
 testpaths = ["tests"]