[BUG] Backend does not validate `startAt` is in the future when creating stream

**Category:** backend
**Project area:** backend/src/index.ts

**Description:**
A stream can be created with `startAt` in the past. This causes the stream to immediately enter an active state with elapsed time, which is confusing.

**Acceptance Criteria:**
- `startAt` must be at least 10 seconds in the future.
- Past `startAt` returns 400 with descriptive message.
- Test added for past start time.