Need help with important information. Can we use BJTs in analog design in sky130 nm?

There’s one in the PDK. https://skywater-pdk.readthedocs.io/en/main/rules/device-details.html#bipolar-pnp-transistor Note that it states

Reverse-active mode operation of the BJT's are neither modeled nor permitted.

However, I have not actually tested a chip with bipolar transistor.

You can, but you shouldn't. BJTs are used in CMOS process for bandgap references, for example. If you really want to use BJTs in your designs, try IHP BiCMOS process. It has proper BJT models.

In sky130, if anyone wants to use BJTs as band gap reference then it should be fine. Is that correct?

Yep. It is their main use