Looks fine to me

I like it the way it is. I think white trim would look too busy with your rug.

Sorry but IMO rooms should have some connection to each other when seen together so since the floors are so drastically different I think I would at least paint the woodwork all the same .

Yes, it looks fine. You've created lovely rooms! Well done.

Both rooms are lovely. But they look like they come from different houses. I don't think painting the trim will do much to change that.

Question... if woodwork is painted white, the frame, cornice and pane inserts would be white, but wood blinds would remain wood.. similar in color to leather sofa and loveseat. Does that sound ok?... and what about bookcase?

What if wall color was changed to match dining/living?

The most obvious thing to do is refinish the floors to be all the same (not ebony). All the paint in the world will not make those rooms flow together without that.

Also, painting the very handsome bookcase is not a good option. Getting a good, hard-wearing paint finish on cabinetry is difficult to do outside of a factory clean-room.

Thank you.