My question, which is still unanswered, is why is there no...

My question, which is still unanswered, is why is there no indication of climate change in the SOI.

If you are really interested in the answer to this question, perhaps this is not the best place to be. My initial honest answer "I don't know". But my curiosity was pricked, and I found an article (in the respected journal "Nature", surely a better place than here) which seems to address this very question. If I interpret the scientific language correctly, the answer is that the El Nino Southern Oscillation Index measures several variables, including those which are less influenced by broader global temperature change, described as "internal" to ENSO.

Having said that, the article cites "evidence of stronger ENSO variability since the 1950s compared with past centuries", contrary to your claim. It also makes a qualified prediction that ENSO will catch up with the other indicators: "...it is apparent that models that best capture key ENSO dynamics also tend to project an increase in future ENSO sea surface temperature variability and, thereby, ENSO magnitude under greenhouse warming."

https://www.nature.com/articles/s43017-021-00199-z