A vector to your camera's right is the same as the forward vector of a camera that's looking 90 degrees further in yaw, and at zero pitch. So you can modify your look vector code to give you your right vector.
var rx = Math.Cos(yaw);
var ry = 0;
var rz = -Math.Sin(yaw);
this._right = new Vector3(rx, ry, rz);
(Here I used the identities that Sin(a + 90°) = ...
At this time and with that error ... you should post this as a issue on github for monogame which is probably the correct place and maybe the only place to get attention from someone capable of giving a answer to this question.
Follow the instructions on the issue submission, if possible make a simplified example ...