In which direction should I carry out a reduction when proving decidability/recognizability?
When we reduce a language A to a language B, we take an instance $x$ of A and transform it into an instance $f(x)$ of B so that $x \in A$ iff $f(x) \in B$. The way to remember that this is the correct direction is that shows you how to decide A if you can decide B. This is the normal, everyday life meaning of "reduction".

The linked answer does exactly that – it transforms an instance of $\overline{HALT}$ to an instance of $L_{all}$, thus reducing $\overline{HALT}$ to $L_{all}$.