The growth of the cloud is exploding overall, with all of the major vendors showing growing lots of revenue growth. Not all of them are profitable, but they are growing. This shows that customers want to use the cloud, and more of them are migrating all the time.
I do think that databases are likely migrated less than many other services, though their use is increasing. Plenty of organizations would like to offload some of the overhead of owning and managing hardware, which may be one reason why the growth of IaaS in the cloud is one of the more popular options.
For those databases that are being used in the cloud, can you guess which ones have the fastest growing usage? Since this is a primarily a SQL Server-based site, you might guess Azure SQL Database, and you'd be close. It's one of the fastest growing, edged out by PostgreSQL. That's one reason we've been publishing some PostgreSQL articles; it's very popular and being used in many organizations that also have SQL Server.
While we know we can build cheaper systems on premises, and we can better control, or at least predict, performance, the cloud is attractive to many businesses. It's not perfect, but it is an option that you should be able to knowledgeably talk about when someone brings it up. That means you need to learn a bit about how it works, the costs, the performance, and the differences with an on-premises system. The options change all the time, so don't rely on your knowledge of the cloud from a few years ago or hearsay. Spend some time asking questions of people using the cloud today.
You also might consider using VMs if someone wants to migrate to the cloud, as the system will appear to be very similar to the way your on-premises instance runs. The hardware setup is different, and you need to learn about the differences in the hardware, especially how you connect disks and their performance.
Knowledge is important, and for many of us, we are looked at as those with knowledge about these different platforms and technologies. That means we need to spend some time learning, and likely a bit practicing to understand the impact so that we can present a good argument about when it may or may not be appropriate to use a cloud database.