I wouldn't change anything except the mirror, vanity, and lighting.

New lighting and new paint colors. I would explore photos to find ones you love. Here’s one I thought was beautifully redone with a small budget. Brb

The (gray?)walls do not seem to go with the (yellow?) floor tiles...and the pictures are not showing enough of the whole bathroom to really see what can be done with what you have...pictures from the door ...showing the whole room if possible...will make it more what kind of mirrors and lighting you have...at a glance the walls that are gray should be closer to the floor color..to make the floors look more intended than just a throwback ..

The original colors would have been bright and vibrant.

Have you considered a little wall-covering archeology to find the original paint or wallpaper? At a hidden part of the wall (we like under the toilet tank), strip off the paint/wallpaper layer by layer until you get to layer 1. That color will almost certainly work and be consistent with the mid-century period.

Another way to find it is to remove the medicine cabinet. If it is original, it has probably be painted around, and the original paint will still be behind the overlay.

Otherwise, I would certainly use peach as suggested by btydrvn with the turquoise tile and lemon yellow with the yellow tile.

I doubt the white wall tile in this room is original.

I live in a house that was built in 1926 and the bathrooms were remodeled about 55. I have since re-remodeled...but that blue tiled bath made me very nostalgic! The toilet and tub are most certainly original as is the wall tile. However the vanity and is newer and perhaps that large mirror. But love the set in toothbrush holders and the soap dish with the grab bar.....and I had towel bars exactly like you have!! Mine was sandle wood and dark brown....and the wall paper was tiny flowers....quite subdued.
If you want to stay true to the period, I would do wall paper.....and a small print.
for the one with the yellow floor, I suspect the toilet in new, It likely was yellow, ans of course the vanity....but the tile is very of the period. I would paint the walls about the same color as the floor and accessorize with tropical green.

I absolutely am in love with your bluish/aqua bathroom. Its gorgeous. The other one is very nice too, but, the blue just has to be my favorite. I think peach would look very nice with it. I also like the idea of a small patterned wallpaper with the color of the tub and floors in it. Actually, that was probably what it had originally. Thank you for keeping them, and not tearing them out. Yours look to be in excellent condition too.

The blue bathroom only needs two new mirrors and two new light fixtures. After removing the large mirror and adding another light fixtures, you will probably have to repaint, but i do like the original paint. The other bathroom I can't tell. Are the floor tiles beige?

The other bathroom the floor is a pale yellow.