It could be a great opportunity for learning, but it's a bit of a red flag that they don't want to give you even a small raise, or change your job description. That makes it sound like they are hoping you will do that "on the side," when in fact it is a full-time position. Hiring you internally will save them a lot of money, so it sounds like they are trying to stiff you.
A lot of people hate Oracle, but if you are curious whether you would enjoy being a DBA, you could explore studying for one of their DBA certifications. It gives you a good idea of how far down that rabbit hole you might want to go. That being said, though, there is no shortage of demand for good SQL developers with a broader development background, especially if you build proficiency with stored procedures. In fact, with cloud technologies taking over a good chunk of the industry, dedicated DBA positions have in fact morphed into more of a sysadmin role. They will never go away completely, but the landscape has definitely shifted.
Bottom line, if you really enjoy SQL, you have some great opportunities ahead if you keep investing in your skills. However, it doesn't sound like your company appreciates those skills as much as it should.
Edit to add: Building and maintaining databases can be super fun when it's less restricted and you feel like your efforts have a direct and positive effect on others. However, the deeper you go, or the larger the organization, the less often you have those opportunities, as the landscape gets stuffier and the requirements understandably become more restricted. I don't mean to scare you away from it, but as a full-stack developer, SQL has never been as fun as it was when I was building useful Access databases at my non-tech internship. Just a heads up.