Early analyses revealed that dark web marketplaces (DWMs) started offering COVID-19 related products (e.g., masks and COVID-19 tests) as soon as the COVID-19 pandemic started, when these goods were in shortage in the traditional economy. Here, we broaden the scope and depth of previous investigations by considering how DWMs responded to an ongoing pandemic after the initial shock. Our dataset contains listings from 194 DWMs collected until July 2021. We start by focusing on vaccines. We find 248 listings offering approved vaccines, like Pfizer/BioNTech and AstraZeneca, as well as vendors offering fabricated proofs of vaccination and COVID-19 passports. Then, we consider COVID-19 related products. We show that, as the regular economy has become able to satisfy the demand of these goods, DWMs have decreased their offer. Next, we analyse the profile of vendors of COVID-19 related products and vaccines. We find that most of them are specialized in a single type of listings and are willing to ship worldwide. Finally, we consider a broader set of listings mentioning COVID-19, in order to assess the general impact of the pandemic on the broader activity of DWMs. Among 10,330 such listings, we show that recreational drugs are the most affected among traditional DWMs product, with COVID-19 mentions steadily increasing since March 2020. We anticipate that our results will be of interest to researchers, practitioners, and law enforcement agencies focused on the study and safeguard of public health.