They started over a policy that wasn't unimportant but clearly not worth like, paralyzing the whole country over. Not that the blame lies with the protestors on that necessarily, the government could have reacted significantly better (and I'm not just saying that, if the rumors are true about the bloodshed). Clearly it wasn't just about the veteran government job guarantee but more generally an upwelling of anger given the material conditions of the population and particularly the youth, which that policy merely coalesced around. It's not an uncommon way for protests to naturally progress; anti-racism protests often center around a single death or set of deaths that were particularly tragic and happened in the wrong place at the wrong time and are emblematic of wider problems; BLM in 2020 for instance. But it is also common in colour revolutions; the Iranian protests over Mahsa Amini are a good example.
Whatever the intentions of the protestors, a clearly worse candidate has now stepped in and the military is in charge, basically. Hasina being forced to leave is only a victory if you're replacing her with a committed socialist, not a neoliberal banker. So either it was a leftwing movement hijacked by liberals, or it was always liberal.