I would check with the supplier or paint shop. Generally, it shouldn’t be an issue. Sealers seal the substrate and provide adhesion for the subsequent basecoats. Just check if you are worried about woodcare, or if your wood is expensive.
It shouldn’t be an issue to apply water-based paints on an oil-based sealer, or vice versa. Theoretically, the oil or water vehicle evaporates, leaving behind the “sealer film or paint film”. Anything applied on this should be fine... I think
If I were to DIY, water-based would be easier to clean, less odour and quicker drying. Oil-based are generally more durable. For high moisture areas, I suggest exterior wall paints that are more water resistant and less chances to habe mould due to added biocides.