I stand corrected, the current Planck analysis seems to take in account that we are moving through the CMB rest frame although I need to read a bit more. It's a long paper [1]
It was the earlier Planck measurements that did not account for this.
This effect seems to be treated and dismissed as insignificant w/r/t the cosmological parameters, in section 3.11 (page 78) of the paper you reference.
There were a lot of new systematic effects in the Planck data, and a lot of the data analysis work amounted to identifying the most significant ones and modeling them out.
It was the earlier Planck measurements that did not account for this.
[1] https://arxiv.org/pdf/1907.12875.pdf