Sorry I think you got confused there by the unclear question in the report. The survey was conducted on 6th of October, one day before the Hamas attack (that's written on the report page). So "this war" can not mean that attack or the Israeli counterattack but probably the decade long conflict.
Also the survey shows people have very low trust in organisations, including Hamas.
The second link they posted is about [1], which was conducted well into the retaliation. So while it is clearly about the October 7 attack, it's also clearly massively affected by the feelings about the counter-attack.
