A 5000 sq ft+ 1920s home is probably super nice. Some areas have lots of 1800 - 2500 sq ft 1920's homes, but a 5000+ house is the real deal. Where is this that is is less the $500k?

You paint the walls (especially the yellow ones) and bring in your own furniture, it will be fine. The wainscoting is a trivial thing. Restoration hardware and pottery barn are hardly formal and they photograph their furniture in similar settings all the time.

What really make a room formal or casual is the home owners furnishings. You will find that if you place more casual furniture and rugs, that your space will be perfect with the molding and the wainscotting. I find wainscoting and molding to be neutral...they can be dressed up to be formal, or dressed down to be casual.