I am not familiar with the baseboard you describe. I feel it must be electrically-powered. Please post a link. It could be a nice electric heater or it could be just marketing hype. Heat generated by electricity can be delivered in several ways. A little blower in the toe-kick or ceiling-mounted heaters delivers hot air. With the electric baseboard, you get natural convection (no blower) and radiant heat. (Radiant is mostly what you feel standing next to a fire your the side facing the fire feeling very warm while the other side can be quite cool.) The last way is by conduction which is the first step in how the floor heater would work. It is hard to say which is more efficient. Electricity conversion to heat is all 100% efficient, but some ways can make you feel warmer with less power depending on how they are being used. When revising the AC did you consider increasing the supply to the bathroom? I guess you just had a replacement system plugged into your existing ducts. Your projects sound familiar to me in my S. Louisiana home. AC is done. Need to do the roof and insulation. Need to take out a pool and regrade the yard. Need to rebuild garage walls. Need to fix the floors. .... It will never end.

If you can remove it, get a can of Rustoleum and spray paint it white. You al;so have the option of using a piece of the wood toekick that matches all the rest of the white trim. If it doesn't come off, I'd get a piece of thin facing -- I wish I could think of what to call it, but I've seen it at Home depot sold in sheets. Some even comes already white. All you'd need to do is have it cut to size and stick on some velcro. The stuff is no more than 1/8 inch thick, so it's not going to stick out. You could also have a piece of metal cut to that size, paint it and stick it up the same way (or with magnets). It's really a very simple fix.

Cleaning around them is the biggest drawback. Sometimes it comes down to Q-tips to get into those spaces. And that is ALWAYS where the cat's toys end up. If you don't do them as integral furniture pieces and instead attach them with velcro, that makes it easier to clean. But you won't 100% get the fine furniture look you pictured.

In a small bathroom the vanity is a great place for storage. The door and draws hide a lot of things. If you do go with the vanity, then the first thing you can do is make the size of the vent cover smaller. It does not have to be that big. It looks like there is no duct installed under the vanity. The air is just coming out from a hole in the wall or floor and into the vanity base. A big hole was cut to fit a big vent. The vent can be half that size for bathroom of this size. You could also install the vent on the side of vanity by the toilet bowl. This hides it when you are entering the bathroom. The air flow might be a little less but it should be fine for a bathroom.