Consider changing Database types to use DateTime<Utc> instead of NaiveDateTime

[jcjones]

Since Clock::now returns DateTime<Utc>, this change pushes the conversion from inside the function to the callers which just moves the complexity around.

I think the bigger question is whether we should use NaiveDateTime from Clock::now, which I was going out of my way to avoid since then we have no timezone tracking.

We could change the database to use Utc though, but I don't want to add that here. I'll open an issue.

Originally posted by @jcjones in #4219 (comment)