Yes, you can run diff-in-diff with aggreggate treatment in this case.
Yes, standard errors should be clustered at the treatment (here=state) level.
No, the number of clusters is not an issue, as the relevant number is the total number of clusters and 50 should reasonably avoid the small cluster problem.
The way you can think about this is to forget states exits. You simply have some (US) observations (firms?) that are treated and others that are not. In principle, that gives you diff-in-diff if you can satisfy all the assumptions on the control group (similar behavior in absence of treatment).
However, three other general problems arise.
Ideally, in this case you'd also want to show results at the aggregated treatment level, which you can't do because of small sample bias, since that gives you only 50 observations in each time period, but that's fine.
Finding the right control units/states (satisfying assumptions, e.g. parallel trends) is hard. The fact that only one state is treated may mean that state is very unique in the context of your research question. Maybe you want to use propensity score matching or synthetic control in addition to diff-in-diff.
Treatments at state level can be very general and you need to ensure other diverging policies also aren't happening etc.
That being said, these types of analyses can be performed and are often done. I recommend finding a paper that does diff-in-diff with treatment at the state level and follow their steps to get you started.