Is sodium acetate a neutral or a basic salt?
Normal salts do not have to be neutral, and vice versa. There are two different features of a salt: (1) containing a replaceable hydrogen, and (2) making an acidic solution in water. They are not necessarily related. For example:


$\ce{NaHSO4}$ has both.
$\ce{NaHCO3}$ has the first and not the second (in fact, being a salt of a strong base and a weak acid, it has to be basic in nature, as you correctly recall).
On the other hand, $\ce{CuSO4}$ is partially hydrolyzed in water solution and hence has the second feature, but not the first.
To make the picture complete, $\ce{NaCl}$ has neither.


Likewise, the opposite features of (1) having a hydroxy group and (2) making a basic solution in water are even less related. For example:


$\ce{Cu2(OH)2CO3}$ has the first feature, but not the second (for it is not even soluble in water).
$\ce{CH3COONa}$ is partially hydrolyzed in water solution and hence has the second feature, but not the first.
$\ce{MgCl2}$ and $\ce{Mg(OH)2}$ form several basic salt phases with both features (J. Chem. Eng. Data 2017, 62 (4), 1384–1396).  They are only sparingly soluble but still form measurably alkaline solutions, especially when warmed.
$\ce{MgSO4}$ has neither.