There are literally dozens of common aquarium plants that do perfectly well in brackish water. It's a total myth that there are not, and one that annoys me profoundly. Many species are in fact brackish water plants in the wild, being either found primarily or frequently in brackish water: hairgrass, Bacopa, some of the crypts, Java fern, some of the Crinum spp, etc., etc.
At 1.003, you can have essentially anything that does well in hard water, so Amazon swords and Vallisneria are both good choices. At 1.005, you'd do best with brackish water specialists, such as those mentioned above. I have my own list here
and one other aquarium forum has an equally good listing, but I'm not sure if I'm allowed to include links to other forums.
The secret is to optimise all the other conditions. If your substrate, CO2 fertilisation, and lighting are inadequate to begin with, adding salt will probably stress the plants to death. But if you have a nice rich laterite and sand substrate, ideally with undertank heating, and increase your lighting to 2-3 watts per gallon, you can grow all kinds of plants in a brackish water aquarium.