The political side sure has some leverage but I highly doubt it would be possible for them to full on block any deal.
Sinwar’s position can be likened to president such as Biden, whereas Haniyeh is more of a negotiator like Blinken.
They might have a slight difference of opinion, but if Sinwar really wanted to accept a temporary truce deal then there is no doubt he outranks Haniyeh.
They have seen how the last temporary ceasefire didn’t achieve anything and was even violated multiple times by israel. So they are now pushing for a full ceasefire deal instead of a truce that only delays the Genocide.