You're stuck in that no-man's land between medical care (which Medicare covers) and dental care (which Medicare doesn't cover). If your oral surgeon is not a physician, whether Medicare covers
your treatment, including hospitalization, depends on the kind of procedure being performed. Medicare considers most work by non-physician oral surgeons as "dental" rather than "medical," and so Medicare doesn't cover it. But Medicare Part B can cover treatment that involves a problem with bones of the mouth and jaw, performed by a non-physician oral surgeon, if it's the kind of treatment that physicians (M.D.s) also perform. If so, the care you receive might be considered "medical" and so would be covered by Medicare Part B even if performed by a non-M.D. oral surgeon (if the oral surgeon participates in Medicare "“ not all oral surgeons do). The problem for you, though, is that you describe the procedure as a "routine extraction". If that's the case -- meaning it's a simple dental procedure, not something that a medical doctor might also do -- then Medicare will not cover it, nor will Medicare cover a hospitalization that is solely to complete this procedure. (If you were enrolled in Alabama Medicaid, they might have better coverage for dental-related treatment, but if you only receive QMB [Qualified Medicare Beneficiary] support, that program will provide no coverage unless Medicare does.)
It's possible, however, that you could find a way for Medicare Part A to cover your hospitalization even though the procedure itself is purely dental. This might happen if one of your medical doctors is willing to write to Medicare to explain that your hospitalization would be due not to the dental procedure itself but to some other serious medical condition -- you've mentioned a cardiologist and a hematologist -- you have that puts you at high risk during such a procedure and so requires your hospitalization. This would require that the doctor provide not only an explanation and request for coverage but also written documentation concerning your medical condition, and would also require cooperation between the doctor and your oral surgeon. This will take some time, but it might result in prior approval from Medicare for the hospitalization, though you would still have to pay the oral surgeon out of your own pocket.