It seems like you are a lecturer at the same place you are doing your degree, but this answer doesn't depend much on that.
You have to start somewhere. And this seems like a low-risk opportunity. You have a couple of things against you, however. One is that you say your field is fairly different from what they prefer. That, alone, might be enough to choose someone else with no negative connotations about yourself.
But the other is that some (probably many) universities prefer not to hire their own graduates. There are important counterexamples, of course. Some people feel that you will gain more from broadening your horizons and that the university will gain more from bringing in "new blood". Again, that doesn't have negative implications about you.
If they will put you in the pool, even as a rather low priority case, you will probably gain important experience from going through the process and dealing with questions in interviews and such, along with preparation of an application. You might get valuable feedback even if you aren't selected.
People are, hopefully, trying to match qualifications to a job description. You may meet them or not. But at the moment tenure track positions are hard to come by and any experience, even with process, is possibly helpful. I'd guess the positives outweigh any negatives.
Your doctoral advisor may have something important to suggest about this. They know the situation better.