STM32F103 - on a 1S LiPo (3.7V)

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Or could it be fed to 5V IN?

No, you can't put 3.7V into the 5V IN, and expect to get 3.3V out.

You could use a zener diode between the + side and the 3.3V pin, to get about a 0.4V voltage drop.