One thing I would strongly suggest for your career, don't get hung up on labels or titles. I was working as a database developer, and by that I mean, designing, building, and coding databases. However, my title was DBA. I even did some DBA duties (on call rotation, stuff like that). The title said one thing, the work said another. It didn't really matter that much. Further, different companies are going to call different jobs by the same title, or have different titles for the same job. It's much more about what you do versus what it's called.
In general, I agree largely with your choice. If a database developer for that company was only ever a T-SQL code monkey, then yeah, I'd skip that too. Just know that other orgs might have a database developer role and you're going to want it based on your stated career goals.
ETL is something I've done quite a bunch of over the years, but it's always been a sideline. Overall in the community, ETL is a specialty. It is one worth pursuing because it will position you well to work with, or around, data science and other analytics if you want to go into that. However, like any specialty, it can also be a bit of a dead end. It's very much a "your mileage may vary" type of situation.
I'd say you're thinking about things correctly. The goal to have a career, versus just a job, is to strive to have three years of experience be three distinct years, not one year repeated three times. Same goes for 10 years & 20. Constant learning and path adjustment is the key.
Best of luck.