I would expect the answer to be (\lambda \gamma^{m})*{\beta}. But, Cadabra gives (\gamma^{m} \lambda)*{\beta}. I think (maybe I am wrong) Cadabra is doing

\lambda^{\alpha} (\gamma^{m})*{\alpha \beta} -> (\gamma^{m})*{\alpha \beta} \lambda^{\alpha} -> (\gamma^{m})*{\beta\alpha} \lambda^{\alpha} -> (\gamma \lambda)*{\beta}.

At the second last step it exchanged the \alpha, \beta indices without worrying about the exchange property of the spinorial index (for example if I chose a basis in which the gamma matrice are anti-symmetric, I would expect a negative sign in the final answer).

Even if Cadabra2 is not following the above sequence of steps, the output is certainly not correct.

Also, just for fun I entered the same code in Cadabra1

{\alpha,\beta}::Indices(position=fixed);

\gamma{#}::Matrix;

\lambda::ImplicitIndex;

ex:=\lambda^{\alpha} (\gamma^{m})_{\alpha \beta};

@combine(ex);

I get the output I mentioned (\lambda \gamma^{m})_{\beta}, which I think is the correct answer. Do let me know what's happening in Cadabra2. Thanks