Fisher & Paykel dish drawers have a salt-dispenser, at least my 2004 models do. They are (were?) designed in New Zealand but sold in the U.S. For a while they were sold rebranded by KitchenAid. My water isn't hard though so I haven't had to use any salt.
(Aside, and I don't know if they are still any good, but these dish drawers are really well engineered. Mine had some problems early on that were resolved by small changes in the design, but FP provided me the parts to retrofit my washers. They've been nearly trouble free since then.)
The H series F&P dishwasher models have a built-in water softener. [0]
According to the user guide, a water softener is recommended if your municipal water hardness is >250ppm which would be quite hard for municipal tap water.
In my region of central Florida the city’s water quality report shows a hardness well below 250ppm, Which you can divide by 17.1 to determine how many grains of salt to take that with.
They were bought out by Haier a few years ago, they still exist as a brand in NZ, not sure about elsewhere. Anecdotally not as good as they used to be.
Available in the UK too. I don't have experience with the drawers (that's the dream though - fridge/freezer especially, drawers for everything (below waist height) makes so much more sense to me) but I'm familiar with a couple of more recent (last couple of years, definitely post-Haier) appliances that are pretty nice. You pay for it though... Seems roughly like Skoda/VW/Audi in terms of top-end F&P branded units with nicer fit and finish than fairly similar but much cheaper Haier branded ones.
I was looking for a fridge-freezer specifically, considered Haier but went with Liebherr in the end - I like that (in terms of white goods/kitchen appliances) it only makes refrigeration units, other than where you use them there's nothing tying them together in why a manufacturer would be good at making them all really, makes sense to specialise in refrigeration, or dish washing, or gas products or whatever IMO.
(Aside, and I don't know if they are still any good, but these dish drawers are really well engineered. Mine had some problems early on that were resolved by small changes in the design, but FP provided me the parts to retrofit my washers. They've been nearly trouble free since then.)