Think of the use of “din/rin” and “pati” as similar to making a list of things. Once you have the first item in the list, the succeeding items are the “ito din/rin” items or the “this too/also” items.
“Pati” is/are the addition/s to the list that came, possibly, as an afterthought or similar to saying “including/in addition”. It serves as an addendum to the original list.
In your sentence, “The test wasn’t hard, even I passed”, I don’t think we’d use “din/rin” nor “pati” for “even” there. That’s because there is no “list” and “even” means more as an exception than a simple inclusion.
If the sentence is “The test wasn’t hard, John passed and Mary too”, we can use “din/rin” – Hindi mahirap ang test, pumasá
si John at si Mary DIN. If after saying that, you realize that you also took the test and passed it, so you may then say “Pati ako. (Including me)”.
With you original sentence, it is more likely that we would use the word “kahit” for “even” – Hindi mahirap ang test, kahit ako pumasá
”. “Kahit” there would be like saying, “(would you believe it) even I passed”, i.e., that outcome was not expected at all.
In the link that you gave and the 2 examples given there:
1. I would translate “Pati mga brief natin ninakaw!” as “Our briefs were stolen too!”, i.e., just adding them to what “they left nothing” really means.
If we are to say “Even our briefs were stolen!”, I think that was meant to suggest that thieves are not likely to be interested in other people’s underwear. So, “kahit” may be more appropriate than “pati” to express that unexpected inclusion.
2. The use of “pati” would be “unnatural” as the writer mentioned because “ako rin” just makes it the “second item in the list” and not an addendum.