Welcome to the Candy Crush Saga Community
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Welcome to the Community,
Sorry to hear about your Problem on Lost Boosters.
When you Uninstalled Candy Crush Saga, the whole Candy Crush Saga data which also contains Booster Data gets deleted because they are stored locally in your device.
This is the only reason for your Problem.
As your Game was deleted from device, your boosters were gone forever. So, You won't get it back despite being installing the Game again.
But Don't Worry About This. You can get new boosters by purchasing them with Gold Bars. And You can Get free Gold Bars here-
https://community.king.com/en/candy-crush-saga/categories/contest
I hope this helps.
I also had this problem. But I won new ones. So You can win them too. Best of Luck for it.
Have A Nice Day!