I'm trying to make a race that starts off with an innate spell ability. Simple enough. Problem is I want the number of uses they get of that spell to go up at certain level milestones. If I just list the spell in the "spells" area and add a new one for each level I get that spell listed multiple times instead of them stacking. When I look in "actions" (which I did notice allowed for overrides at higher levels) there is no way to input the spell without literally remaking it. Am I missing something obvious?

TLDR; how do I make a race with limited use access to a spell gain more uses of said spell as they level up?

You can't easily. If you use the Spells modifier, the only knobs for limited uses are (some fixed number) + (an ability score modifier)

You can make an Action for tracking uses. Those have better control of limited uses as you level.