can't quit understand one step of the recurrence time complexity calculation
It obviously is not correct. To fix it, define $S(m)=T(2^m)$, and then we would have $S(m)=S(m/2)+1$. Now, continue with the proof replacing everywhere $T(m)$ with $S(m)$. After you solve what $S(m)$ is, substitute $m=\log(n)$ in the solution to get what $T(n)=T(2^m)=S(m)$ is.