When I was starting my career, I expected to be a programmer. That's what people who wrote the software were called. At some point they adopted "developer" instead, shunning the programmer label. Now I see software engineers has replaced developer in many organizations. I'm not sure the job is much different than it was in 1990, other than the specific technologies used.
The DBA used to do a lot of system administration-type work on database instances. Check logs, set security, run backups, and maybe look at some queries. However, in many cases, their work was limited to things running inside the database software, or the database software itself (patches, related configuration for the host OS, etc.).
I saw recently that DBAs have started to adopt the data (or database) engineer label as a new job description. Presumably, this pays more because, well, it sounds like it should. Data Professional sounds more comprehensive and skilled than Database Administrator.
Is it? I do think that many people working with databases are being asked to learn and do more (and new) tasks as a part of their daily work. We often need to support and maintain a wider variety of different systems. If it's the same platform, then we often support more versions, especially with the 2-3 year cycle of releases of SQL Server. However, we may also need to learn a bit about other platforms, like Oracle, MySQL, PostgreSQL, etc.
Adding the ability to work with and deploy new languages, like R or Python might help us land a new position. Certainly understanding cloud database platforms and options, their deployment, and monitoring can be useful in asking for a raise or interviewing for a new position. Scripting, PowerShell, and DevOps are good skills as well.
Why bother? Especially if you have a good job and are comfortable. You never know when things will change. Your company might downsize, as Ken's did. They might get bought by another organization and your job could change (or disappear). It's possible that family or some other situation might make you look for a different situation. There are lots of possible reasons why your current job might change.
If you want a better job, perhaps more compensation, better hours, remote work, less late night calls, or something else, then it's not a bad idea to beef up your skills. Learn to automate things in a better way, which might make your current job easier. Experiment in the cloud, maybe do a small PoC of how you might move or deploy a current workload into a VM, a PaaS service, or even a new platform. Can you migrate from one database platform to another? That's a useful skill.
I have found that a lot of the really good jobs are a hodge-podge of different skills. Being adaptable, comfortable learning, and trying to grow are important skills to demonstrate. Even more important, learning to talk smoothly with others about why you made a decision or recommend something is a key skill to getting hired.
Sprucing up your titles can help, especially with HR where new titles often mean new salary ranges. SRE Engineers were only at Google at one point and their high salaries set a bar. Engineer, Scientist, Architect, these are all better than Administrator. Boost your skills (tech and soft) and you might find a new position that is even better than the one you have today.