got a statistically significant R-squared value of -0.049.

That's r, the correlation coefficient, not R^2 the total variation explained (which, being squared, can't be negative). For a simple regression (one var regressed on one var), R^2 = r^2 which, in this case, would be (approx) .0025 meaning that pitch tempo explained less than one half of one percent of the total variation in OAA.

Pitch tempo measures the median time between pitches within a plate appearance and breaks those down by bases empty and runners on base situations at both the individual and team levels. I calculated a weighted average of the bases empty and runners on situations to get one tempo mark at the team level for each team season since 2016 (210 seasons in all) and compared that with each team’s OAA marks from those seasons.

I would not have done the analysis this way. Team weighted average median pitch tempo (the complexity of that name hints at a problem) likely doesn't vary much from team to team -- basically it's only capturing something if there are slow-pitching teams and fast-pitching teams. There might be some variation due to particular pitching coaches really stressing tempos but I'd imagine most teams are a mix of faster and slower and mainly average tempo pitchers so it pretty much washes out.

Further, the old adage was never about "this team pitches slowly so the fielders are asleep on every batter." It has always been about individual pitchers. And to the extent that's a problem, I suspect it's more that this pitcher is slow all game long or that any effect kicks in only in long innings. That suggests some sort of PA by PA analysis, preferably that includes measures of the total time of the last two PAs or elapsed inning time or something as an extra explanatory variable. Then possibly aggregation by (starting) pitcher.

R^2 the total variation explained (which, being squared, can't be negative)

Unless you're evaluating the Athletics, in which case that squared value could be negative. Because their defense is imaginary.

Further, the old adage was never about "this team pitches slowly so the fielders are asleep on every batter." It has always been about individual pitchers. And to the extent that's a problem, I suspect it's more that this pitcher is slow all game long or that any effect kicks in only in long innings. That suggests some sort of PA by PA analysis, preferably that includes measures of the total time of the last two PAs or elapsed inning time or something as an extra explanatory variable. Then possibly aggregation by (starting) pitcher.

Even just looking at overall average tempo for different pitchers on the same team seems likely to be a better approach, because that should largely account for variations in team defensive quality. (With whatever caveats are needed - a fast-tempo fly ball pitcher vs. a slow tempo ground ball pitcher could mess with the results if the team's outfield is notably better or worse than its infield, for instance.)

this is completely anecdotal, of course, but the Indians made an inordinate number of infield errors playing behind Sudden Sam--and, at the time, it was ascribed to them being back on their heels because of the way McDowell dawdled on the mound and walked so many batters