Assignment of the 13C NMR spectrum of 4'-bromoacetophenone
Maybe this isn't the answer you are looking for, but $\ce{^13C}$ NMR shifts are often not amenable towards analysis via electron-withdrawing / electron-donating effects—in my experience this is especially so for aromatic rings. Any such analysis is quite unreliable and can lead to wrong conclusions if you try to use it for assigning peaks.
The numbers that ChemDraw predicts are based on empirical tables of chemical shift corrections. These are experimentally observed chemical shift changes that occur at each position of the benzene ring upon substitution. For a ring with multiple substituents you can approximately add these up. See e.g. Hans Reich's website for such tables.
See also long's answer to &quot;Assigning the 13C NMR spectrum of bromobenzene and 4-bromobenzophenone&quot;: although most of the discussion is on the ipso carbon (C6 in your labelling), the general point is the same: it's often not trivial to rationalise or predict chemical shift changes in aromatic rings.
[There might be more sophisticated theoretical analyses out there based on diamagnetic and paramagnetic shielding arguments, but I'm unfortunately not aware of these.]