How to define an interface for objects with dynamic keys?

Your object looks like a dictionary of Object arrays

interface Dic {
    [key: string]: Object[]
}

The typescript literature often refers to this pattern as "the description of an indexable object" with a general form

interface Dic {
    [key: string|number]: object_type
}

type Dic = {
    [key: string|number]: object_type
}

There's now a dedicated Record type in TypeScript:

const myObject: Record<string, object[]> = { ... }

Also, consider typing the keys whenever possible:

type MyKey = 'key1' | 'key2' | ...

const myObject: Record<MyKey, object[]> = { ... }

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