HD wallet: Can an external party relate addresses?

Any technical detail is appreciated

The most common forms of address in Bitcoin (e.g. P2PKH) are the result of a hashing operation using hashing algorithms like SHA256.

As a random website put it:

There are four main characteristics of a good hash function:

1. The hash value is fully determined by the data being hashed.
2. The hash function uses all the input data.
3. The hash function "uniformly" distributes the data across the entire set of possible hash values.
4. The hash function generates very different hash values for similar strings.

(my emphasis)

So the hashes are indistinguishable from random numbers. Which means you cannot learn anything about the original data by studying them. You cannot tell if two hashes are the results of data that differs by one bit or by a million bits. You cannot tell if two hashes are related. You cannot tell if two addresses are related only by studying the addresses.

Similar characteristics apply to public-keys and some other interesting numbers appearing in the public replicated journal of transactions known as the Bitcoin blockchain. I believe the process that produces a private key or a public key is intended to produce numbers that outside observers will not be able to distinguish from numbers produced completely randomly.

For example given these numbers
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From anything above, there is no analytic way to tell how they are related

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