The simplest way to transfer torque between the two rollers is with a large diameter, thin wall, “torque tube”. When transferring torque, the material nearest the neutral axis is not helpful.
Your picture shows only a thin rod, which has only the material closest to the neutral axis. That is exactly the wrong way to do it. A thin rod would be a twist or torque spring and could easily fail. The rollers will need to slip against the belt to protect the connection rod from damage.
There are many other mechanical solutions. For example a stepped pulley on each roller, connected by a stepped belt, that passes around diagonal rollers, to turn the belt through 90° at each end.
There are also electrical solutions. For example, you could mount a shaft-encoder on the master roller, then drive the other roller with a servo motor as the slave.
Why do you need a connection?
Does the connection drive one of the belts from the other?
How much torque do you need to transfer between the rollers?
What are the length, diameter, and separation dimensions of the rollers?