Nested array operation for $all does not seem to work in mongodb

Working with Data
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1

I am trying to find documents where any or all nested array elements must contain at least the values provided. This can normally be achieved easily with the $all operator. For example here:

[
  {
    "words": [ "Hello", "World", "!"],
    "wordArrays": [
      ["Hello", "World", "!"],
      ["The", "Sun", "Shines"]
    ]
  }
]

The query {words: {$all: ["Hello", "World"]}} correctly matches because both are contained and {words: {$all: ["Hello", "I do not exist"]}} does not match. So far so good.

If you attempt the same for the nested arrays this stops working altogether. {"wordArrays.0": {$all: ["Hello", "World"]}} does not match. I have found similar questions why on nested arrays all the operators start to fail but no one ever can explain why and they just use $elemMatch. But I do not know how I would translate my “all values must be in the array” to an $elemMatch. And then how I would say

  1. ANY of the wordArrays must contain “Hello” and “World” → would match
  2. ALL of the wordArrays must contain “Hello” and “World” → would not match the data

I have prepared this little playground with the data in the hopes somebody knows how to achieve this.
Playground

I would prefer if this could be solved all within the Find() stage, but if operations like this suddenly require the aggregation pipeline I am fine with that too.

My approach for ANY match does not return any matches, and I do not understand why {wordArrays: {$elemMatch: {$all: ["Hello", "World"]}}}. I read it as wordArrays: does any element match: array contains “Hello” and “World”. And that should have matched the document

Thank you!