Why is this language Turing recognizable and not not-Turing recognizable
What you are missing is that if $\langle M, w\rangle \notin \overline{A_{\mathrm{TM}}}$, i.e. if $M$ halts on input $w$, you don't know whether or $M_1 \notin L$. If $M$ does halt on $w$, but this takes longer than $20$ steps, it would also hold that $M_1 \in L$. Thus, you don't have a reduction here.
That the language $L$ cannot be co-RE is an immediate consequence of Rice's theorem.