What is Bearer Context Setup Request in 5G E1AP?

It is the E1AP message the gNB-CU-CP sends to the gNB-CU-UP to create the UE's bearer context on the user-plane side.

Who sends Bearer Context Setup Request?

The gNB-CU-CP sends it to the gNB-CU-UP over the E1 interface.

What does the message mainly carry?

It mainly carries the UE identifier plus the bearer-context setup payload that defines session, DRB, QoS, and transport-related user-plane state.