THis is what made me think that the combo is all wrong

No

Can I stain with oil and finish with water based on wood floors?

No, you cannot stain with oil and finish with water-based on wood floors. The two types of stains are incompatible due to their different chemical compositions. Applying a water-based stain over an oil-based one can lead to poor adhesion, color inconsistency, and a blotchy finish. It is recommended to stick with one type of stain for optimal results and to avoid mixing them. engineerhardwoodflooring.com

yes, i think it can be done if the stain is given enough time to dry.. But, the question is - does oil-based stain cause the same kind of yellowing effect that oil-based poly does?

And, are there cons to using water based stain and water based poly - and avoiding oil-based anything? I just don’t want my floors to yellow over time..:

It's the poly that yellows over time, not the stain. There are new polyurethanes that do not yellow like grandmas used to.

From what I understand, no the stain will not cause yellowing, that is a product of the polyurethane top coat.

Thank you so much!!