[Yuri]

4-county Pittsburgh growth (2020-1950):
+0,81% -3,39% -2,93% -7,35% -5,72% -0,17% +8,68%

Butler County growth (2020-1950):
+5,39% +5,62% +14,52% +2,77% +15,61% +11,60% +17,80%

That's a massive difference, one of the most extreme you can find in any metro area. And size alone doesn't explain it. There are plenty of very small counties in the western half of PA posting negative growth since the 1930's or earlier. The neighbouring Armstrong County, for instance: peaked in 1940 (!!!) and with less people in 2020 than it had in 1910 (!!!).

Or Butler had/has a very good reason for being growing on its own (a farming powerhouse centered in Butler city, I don't know) or it's indeed Pittsburgh spilling over it since 1950.