fix(api): a non-finite number in a JSON body is refused with a 422, not a 500

The JSON parser under FastAPI accepts `Infinity`/`NaN`, and both progress checkpoints truncate the
position with `int()` — a hand-written checkpoint came back as a 500 with a traceback. Their bodies
now refuse non-finite floats, and the app's validation handler — FastAPI's own shape — echoes a
non-finite input by name: the default one failed to serialise its own error (JSON has no NaN), which
was a 500 by another route. Sibling of the subtitle routes' non-finite query parameters.

backend/app/main.py

@@ -1,10 +1,13 @@
 import asyncio
 import logging
+import math
 import sys
 from contextlib import asynccontextmanager, suppress
 from pathlib import Path
 
-from fastapi import FastAPI, HTTPException
+from fastapi import FastAPI, HTTPException, Request
+from fastapi.encoders import jsonable_encoder
+from fastapi.exceptions import RequestValidationError
 
 # When started via uvicorn --log-config the "siftlode" logger is already configured
 # (see log_config.json). This block is a timestamped fallback for other entrypoints
@@ -112,6 +115,19 @@ async def _sweep_hls_orphans() -> None:
 
 app = FastAPI(title=settings.app_name, lifespan=lifespan)
 
+
+@app.exception_handler(RequestValidationError)
+async def _validation_error(request: Request, exc: RequestValidationError) -> JSONResponse:
+    """FastAPI's own 422, in its own shape — except that it can be ENCODED. The JSON parser accepts
+    `NaN`/`Infinity`, a float field refuses them, and the refusal echoes the value back: the default
+    handler then failed to serialise its own error (JSON has no NaN) and the request became a 500
+    with a traceback. A non-finite value is echoed as its name instead."""
+    finite = {float: lambda x: x if math.isfinite(x) else str(x)}
+    return JSONResponse(
+        status_code=422, content={"detail": jsonable_encoder(exc.errors(), custom_encoder=finite)}
+    )
+
+
 app.add_middleware(
     SessionMiddleware,
     secret_key=settings.secret_key,