What led to the progress in the Hamas-Israel hostage exchange negotiations after earlier threats to halt the release?

After a period when the hostage exchange talks appeared stalled, significant momentum was built through diplomatic efforts. Initially, Hamas had threatened to withhold hostage releases, claiming Israel wasn't fulfilling its ceasefire obligations regarding displaced Palestinians in northern Gaza. The breakthrough came through extensive back-channel negotiations facilitated by Qatar and Egypt, who worked to overcome the negotiation snags. Despite strong language from all sides, these mediation efforts have successfully moved the talks forward, resulting in Hamas's agreement to release six Israeli hostages and the remains of four others, including members of the Bibbus family. This progress indicates the negotiations are now moving in a positive direction.