What if the Rebellion of the Seven States brought down Han and started the Warring States Period all over again?
I don't think that would happen. In order to survive, I don't think the seven rebelling states could survive unless they do something drastic. The seven states controlled a decent amount of land and power, but not a majority. The centrally-held areas under the commandery system, answerable only to the Emperor, was at least one third of the Han Dynasty and maybe up to one half. I've seen differing estimates. The seven states did not make up even the majority of the subordinate kingdoms. The commanderies, combined with the loyal princes, will be overwhelm the seven states unless the latter do something drastic, perhaps taking Chang'an. And if that happens, what's to prevent one of the leaders, perhaps Liu Pi, King of Wu, from simply trying to take over the throne itself?
The only way you could get a prolonged period of division is if the seven states manage to end the commandery system and turn the rest of the Han Empire into subordinate kingdoms, leaving the Han Emperors only with control of the Chang'an area. But that would require the rebel leaders to decide who to enfeoff, which would probably provoke dissent amongst themselves, which would give the loyal Han forces a chance to regroup and win. It would also require the rebel leaders to give up their own chances of being Emperor in order to stay merely feudal leaders.
If you want to create another Warring States situation, you'd need something extremely provocative, one with a point of divergence before the Rebellion of the Seven States starts, not afterwards. For example, if Liu Bang or one of his sons announces the abolition of all kingdoms, period. That might lead to enough unrest to keep China divided.