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You can have set theories that allows sets to contain themselves without allowing Russell's Paradox. You can read about non-well-founded set theory[1] if you're curious.

[1]: https://en.wikipedia.org/wiki/Non-well-founded_set_theory

I like the diagram of "the set containing itself". It illustrates non-well-foundedness niceley.

Which diagram are you referring to?

This one:

https://abuseofnotation.github.io/category-theory-illustrate...

Resolving this paradox is discussed in TFA as being the founding rationale for the Zermelo–Fraenkel set theory in fact.

simple: there is no such set.