Closed-loop pole moving to RHP - less stable or more stable?
You are comparing a first-order system with a second-order system.
The first equation you show (10.4) describes a first-order system. The pole moves farther along the negative real axis as you increase the feedback, as the text describes.
The Bode plot in and discussion around Figure 10.7 is a second-order system. In a second order system with real open-loop poles, the poles first move toward one another along the real axis with increasing feedback, then after meeting along the real axis, move away from one another in the positive and negative imaginary directions. Thus the angle they make with the imaginary axis is decreasing, leading to a less stable system with increasing feedback. Thus the Bode analysis and the root-locus are consistent.