im trying to figure out how stats are passed down. does leveling up pets/raising their stats influence their offsoring at all? or is it based purely on base stats?

the only difference levels make is that higher level pets' offspring will start with up to like... 5? levels (not sure on the maths, but what level exactly the parents are affects it)

stats are inherited as "parent A has x, parent B has y, pick a number in-between"
eg, A has 20 base Str, B has 23 base Str, babies could have 20, 21, 22, or 23

See more on sylesti genetics here (post 4 in this thread covers this a bit also, important bit is that stats are arranged "Active Stat (Base Stat + Grove Stat)" so a pet that has "Strength: 231 (31 + 30)", 31 is the one that passes down like that (the +stat does sort of the same but a bit differently, see post 4)

From there base stats can be increased only via the manual hatching options, and via nurtures to hatchling stage sylesti (see posts 5 and 6 in the guide)