* Change in engagement for posts by Elon Musk
* Change in engagement for republican content
It seems to me that when taken together, these two make a fair case that there was a change in algorithm on the given date?
Besides, the study you are claiming "is not science" did not even make strong claims as to there being an algorithm change. The study made an analysis, and concluded that they might point towards there being an algorithmic change.
Additionally, as you say "If the claim is that Musk tuned the algorithms at that special date, you have to prove it by other means". What other means exactly? We have no data to go on except observations of what happens on the platform. From the information we have it seems like everything points towards this being the case.
The case for manipulation happening furthered even more by Elon Musk repeatedly showing he is full of shit, and has no qualms lying and totally making stuff up. (see his repeated lies about Autopilot, his lie about being world class at video games, his lies about DOGE cuts, etc).
Before dismissing these findings, ask yourself honestly: would you apply the same rigorous standards of proof if the algorithmic changes benefited different political figures or viewpoints?