Say we have a short exact sequence $$0\to A\xrightarrow{i} B\xrightarrow{p} C\to 0$$ of $C^*$-algebras, where $C$ is unital. Suppose there exists a section $s\colon C\to B$ so that $p\circ s=1_C$, i.e. the sequence splits.
Question: When does this imply that $A\oplus C\cong B$?
One can see that this isn't always the case by considering the sequence $$0\to A\to\tilde{A}\to\mathbb{C}\to 0.$$ Then if $A$ is not unital, $A\oplus\mathbb{C}\ncong\tilde A$, since the left-hand side is not unital. Yet from this question it seems that we sometimes do get a direct sum from a short split exact sequence.
Added later: I think the answer to this question should be simpler. Namely, if there exists a section $s\colon\mathbb{C}\oplus\mathbb{C}\to C[0,1]$, then it must take the projection $(0,1)$ to a projection in $C[0,1]$ taking the value $0$ at $0$ and $1$ at $1$, and there is no such function.