I am new to overseeding. I just spread the seed on the lawn, and am watering it. Is that okay? Should I do something differently?
The soil quality looks okay. Because you already seeded, I'd say just keep it damp until germination. It's pretty simple. If you want, you can fertilize with something suitable for young grass before winter (lower nitrogen requirement, and preferably accessible calcium). I use 6-12-6 + Solu-Cal. This step isn't entirely necessary, but gets the new grass established much faster.
And the seeding job looks okay, knowing that you really can't work the soil much before overseeding. But it looks like you've top dressed with topsoil, so you probably could've worked out more of the lumps first. That way you can lightly rake in the seed, and it will germinate more uniformly. But as I said, as the job is done, watering, and possibly fertilizing, is all that's necessary.