Adding water to the bottle only make the shampoo thinner so it flows easier. If you had no problem getting the shampoo to flow through the sprayer, then all is well.

I think my lawn suffers from hard soil too. I dormant-seeded last fall. Will this shampoo application have any negative effect on the new grass seed, which has not germinated yet? Thanks!

I would not think so. And I have not read anything from others on that topic. If you are worried about it, wait until after you are mowing.