Provider

The dictionary of the few labels the kit says itself — undo, the hint bulb, the secret field. English without a provider; lang="cs" switches the whole set.

When to use it

A Czech application: wrap the tree in <IngotProvider lang="cs"> and the toast, the hint and the secret field speak Czech with no further props.
An application in a language the kit does not know: labels overrides single labels and the chosen lang fills in the rest.
A primitive of your own that has to say a label itself — read it from useIngotLabels(), not from a constant.

When not to use it

Page text, buttons, headings — that is content the caller supplies translated. The provider carries only the labels the kit would otherwise say itself.
One component should speak differently from the rest of the page: use its own prop (undoLabel, bulbLabel, secretPlaceholder) — it always wins over the provider.

Properties

lang: "cs" | "en" — The built-in dictionary to start from. Defaults to en.
labels: Partial<IngotLabels> — Overrides for single labels; whatever is missing comes from lang.
children: ReactNode — The tree the dictionary applies to — typically the whole application.