They were hamstrung by more than Manchin so I don't really know what your whole spiel there is. Its interesting that you can clearly see how Republicans are "fucking things up at all costs, especially if its anything at all popular with Democrats" but still want to blame Democrats. Doubly so considering the wealthy hate raising the minimum wage almost as much as any other single issue outside of closing tax loopholes or raising taxes that affect them. That you clearly see that but want to pull a "both sides" argument out of it is so fucking stupid, that, well, its why we are where we are politically.
Even if Dems had raised the minimum wage, some random asswipe that applied to franchise a fast food restaurant 30 years ago, backed by Ginni Thomas, probably would've sued and gotten the Supreme Court to rule it violates their 1st Amendment rights or some bullshit.