An individual drives into an apartment complex, of which they do not reside, and adds an item to the recycling bin. This occurance is hypothetically during COVID-19, during Washington's "Stay Home, Stay Healthy, Stay Safe". Are there legal grounds to punish?
Punishment is probably not possible, though there are so many recycling schemes in the state and the law changes in three waves this summer: it depends on where this recycling comes from. As described, it does not constitute "dumping". The lockdown does not contribute anything (it is not a punishable offense to be outside or to put stuff in a recycling bin). State trespass law does not clearly apply, since it requires knowingly entering upon premises (still, a prosecutor might creatively argue that it is). There might be local ordinance.
The owner of the complex could sue the errant recycler for damages, depending on what harm was done. In a worst-case scenario, the substance could be something illegal to recycle and the owner could be fined, so the owner could sue to recover for his loss. Since most recycling schemes don't restrict you to just what fits in the bin, the "used up our space" argument doesn't work, but there is a small chance that addition of legally-recyclable material could make other material not recyclable on this run. (Civil liability is about compensating a person for the damage that you did, whereas punishment is about the government meting out a statutorily specified consequence for committing a crime; being required to pay damages is not a punishment).