Can I connect my battery to the 3V3 pin?

No, absolutely not.

The 3V3 pin bypasses the onboard 3V3 LDO regulator, and if you connect a battery that can be as high as 4.2/4.3V, you could potentially damage components on the 3V3 rail.

Since lithium batteries can reach voltages as high as 4.2-4.3V, connecting one directly to this pin risks damaging components designed for 3V3 operation, including the ESP32 chips themselves.

For proper battery power, please see the Powering your board from battery article for safe connection methods.