The insulation is provided by wire enamel only, so is only suitable for Functional insulation. So if you have a gate driver that's power line referenced, driving an inverter that's power line referenced, you're fine; but if the driver is SELV referenced, you must use Basic (if grounded) or Reinforced (if isolated).
As mentioned, flux (ET) is small, so you're most likely to succeed with a low voltage, low impedance driver; which is the intended use, after all. You'd then need a differential receiver and gate driver on the isolated side.
Power transfer capability isn't much, and you'll need to do it at a pretty high frequency. Which may prove lossy. I would be surprised if you could push 1W over a single transformer without it being unacceptably poor in performance (low efficiency or excessive temperature).
Some common mode chokes are reasonable for such purposes, having excellent isolation voltage capacity. (I once hi-potted a ~13mm split-bobbin part up to 12kV!) But they have a high coupling impedance (due to the relatively large leakage inductance), which limits bandwidth and power transfer capability. A watt or two is reasonable. Because the core is ungapped, and each winding is not tapped or split, you must use a full bridge forward converter topology.
Tim