The Qataris froze their mediation efforts because they saw that the two sides were not prepared to reach an agreement.
Egypt is continuing to mediate. Now is the time to open a direct secret back channel between Israel and Hamas.
Direct contact can be freer to explore new possibilities, with built in deniability. Each of the sides blamed the other for blocking an agreement. Both sides are responsible.
Hamas wants the war in Gaza to end. Netanyahu does not. Hamas wants to free Palestinian prisoners. Netanyahu does not want to release Palestinian prisoners. Israel wants the hostages home. Hamas is not willing to release any hostages without a guarantee that the war will end and Israel will withdraw from Gaza. Israel does not agree that Hamas will continue to control Gaza after the war. Hamas seems ready not to control Gaza, but in the Hamas-Fatah negotiations, Fatah is not willing not to control Gaza either.
There must be a non-partisan Palestinian civilian government in Gaza which is not Hamas and not Fatah and has control over everything – including the security forces, without that there is no possible agreement in sight.
There is room for negotiations and possibilities for reaching agreements, but the negotiations must be ongoing without stop and they must be conducted as directly as possible. That is my experience in reaching breakthroughs.