Big thanks to @jcalz, whose answer set me on the right path!

I was getting some strange behavior when arrays are involved. I think what was happening is that the resulting type was including a union of array properties. This could be what @jcalz was referring to when they said:

\> you will probably have some use cases where this definition does things you don't expect or like.

Here's an example of the array index / property issue I was facing:

result:
albumMedias: number | ShareAlbum_shared_album_album_medias_cursor_album_medias[] | (() => ArrayIterator<never>) | ... 38 more ... | ((index: number, value: never) => never[])

I modified the solution to properly handle arrays without including all the Array properties.

type GetDeepProp<T, K extends string> =
  K extends keyof T
    ? T[K]
    : T extends Array<infer U>
      ? GetDeepProp<U, K>
      : T extends object
        ? {
          [P in keyof T]:
          P extends string
            ? GetDeepProp<T[P], K>
            : never
        }[keyof T]
        : never

Thanks @jcalz!