I mean: does encrypting data multiple times have an effect on diffusion and confusion? Does it increase security, or does it have no effect? Is it useless? Does it make it harder to break the secret, or not?
Yes, multiple layers of encryption using different algorithms and different keys make the encryption as hard as the hardest in the chain.
IIRC this was adressed in Bruce Schneier's book Applied Cryptography (2nd edition).
But the important part is to use different algorithms, or at least different keys. Algorithms that use "round keys" are often optimized for a number of rounds. Using the same key will not necessarily make the message harder to break, and can theoretically make it easier.
A nice example is Triple-DES. Encrypting a message, then encrypting it again with a different key was vulnerable to meet-in-the-middle attack and effectively added only 1 bit of key space. Instead, it was found that one had to encrypt a message, then use the decryption algorithm but with a different key, then encrypt it again.
Even with 3 independent 56-bit keys, the effective key size is 112 bits as it is vulnerable to a meet-in-the-middle attack (source: Wikipedia).
So the strongest way is to use different keys and different algorithms.