Can you create a small 2" thick mounting block to put behind the posts to bring the towel bar forward? Cut a circle the same size of the post so you don't really see it or make it larger so you could router a decorative edge on it to make it look intentional or bevel it so it seems to melt into the wall .

Use coat hooks, instead. Or buy a double, and only use the front bar. Or Buy a free standing towel bar. Or use a swivel configuration.

Thanks for the ideas. I have a 6x11 bathroom and it’s along the side wall so any extra bracket would be noticeable. Shoot! I was hoping to just find a deeper bar, like in the guest bath. Someone used to make them—we have (or had) the technology!

This isn't 4" but it's 3 5/8". Only off by 3/8". https://www.harneyhardware.com/products/towel-bar-30-in-savannah-bathroom-hardware-set-satin-nickel-16180?