I do not know whether hard water is suitable for watercolor usage or if it will cause any damage to the color when it comes to archival quality. If it does cause damage, are there suggestions for improving the use of hard water with watercolor?
Hard water will work fine.
However, as with all impurities, the minerals it contains will have an impact on both the purity of the colours and the texture of the paint.
Hard water contains relatively high levels of calcium and magnesium, known for causing buildups of limescale: as the carbonates are deposited, they leave an insoluble off-white residue. This residue can have an impact on the colours and transparency of watercolours (and water-soluble oil paints), with slight variations between different pigments, I presume.
In most cases, however, I presume the impact is indiscernible.
Harder water will increase the granulation of pigments in water colour, which may or may not be a desired effect.
This blog post recounts the experience of using a paint described to be non-granulating which resolutely would not have behave this way, and it turned out this was caused by the use of hard water. The accompanying picture also clearly illustrates the difference between using hard water or distilled water:
Since hard water is hard to soften, using a different source of water is the easier option.
As fixer1234 mentioned in the comments, the best way to prevent any deterioriative effects from using hard tap water is to use distilled water, which is usually easy to come by, cheap enough not to risk your watercolours losing some of their vibrancy, and free of any contaminants.
As mentioned in this Wet Canvas thread, it can also prevent the watercolour from granulating altogether: if this is undesired behaviour, it is suggested to use filtered or purified water.