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This might a long read but it is well-written reader-friendly analysis of Tarjan's proof with chain of reasoning. https://codeforces.com/blog/entry/98275

Robert Sedgewick has a great explanation in his Algorithms book. He has gorgeous diagrams alongside his explanations.

Is it in an old edition? I just downloaded an extremely legitimate version of Algorithms 4th edition but it has no section on union data structure.

It should be in Chapter 1 Section 5 of the 4th edition. It's even in the table of contents.

Sorry, my bad. I searched for the word "disjoint" expecting it to be prominent in this section but somehow this word only appears 3 times in this book non of which are in this section!

Anyway, while the figures in this work were indeed gorgeous, it was not what I was looking for. It did not even contain a non-intuitive analysis of the inverse ackermann complexity, much less an intuitive one!

Here's a writeup I made a while ago: https://www.overleaf.com/read/hjbshsqmjwpg