Your numbers are not even close.
> In 2019, the GDP per capita (adjusted for purchasing power parity) was $36,701 in Lithuania, $35,853 in Estonia and $30,830 in Latvia.
Source: https://wedc.org/export/market-intelligence/posts/strong-gro...
Botswana has a $7,347.55 GDP per capita according to Google (in 2021).
That's at least 75% lower than the worst Baltic nation, not "slightly below."
There's plenty of factors that helped, I can think of a dozen right off the top of my head, but the one that made a crucial difference is in my opinion really the above.
Basically this: https://en.wikipedia.org/wiki/Seretse_Khama#Presidency
South Africa also props Botswana up via a customs union.
https://www.tralac.org/news/article/6931-surge-in-botswana-s...