Autofocus first admin input with useRef

## Goal
When the admin form mounts, automatically focus the first input via `useRef`. Teaches `useRef` for DOM access vs. holding state.

## Acceptance criteria
- [ ] `useRef` is wired to the first input
- [ ] First input is focused on mount
- [ ] No re-renders triggered by the ref

Locate the admin form and its first input, then read the surrounding component to see how it mounts. Wire the typed ref and verify that the first input is focused on mount without the ref triggering re-renders; the acceptance criteria define when the work is done.

Written by the indexing model from the issue text.