Originally posted by Nesano:

I got some sorta-data and I'm not convinced damage or tool level plays a role in seed drops.
...
Must have been getting some weird RNG because seed yield has been trending upward whether I use a bronze axe, a flint axe, or other trees to harvest trees.

This has been my experience, as well, but it's good to see some confirmation.

RNG takes a lot of samples to get a good feel for, especially when the randomness is complex. That is, you're looking at the output and trying to determine the chance to drop any seeds vs the chance to drop multiple seeds, and this is all complicated by having multiple chances to drop seed(s).