Have you seen Packer-Raeburn Stabilization trick?

Judith A. Packer and Iain Raeburn, *On the structure of twisted group $C^*$-algebras*, Trans. Amer. Math. Soc. **334** no 2 (1992), 685-718, doi:10.1090/S0002-9947-1992-1078249-7

Specially Theorem 3.4 therein establishes that the algebra is Morita equivalent to a Twisted Group $C^*$-algebra, summarizing the answer by N. Ozawa and the correction above.

By considering the trick of viewing the algebra $K\rtimes G$ as a locally trivial bundle with a $G$-action over a contractible $G$-space $X$ (for instance, the total space of the universal $G$-Bundle $EG$, but also the space $\underline{E}G$ works), you can see the $C^*$-algebra in question is Morita equivalent to the algebra of sections of the Fell bundle over the transformation groupoid $X\rtimes G$. This has been documented in Kumjian's monograph

Alex Kumjian, *On equivariant sheaf cohomology and elementary $C^*$-bundles*, J. Operator Theory **20** (1988), no. 2, 207–240 (journal pdf)

Other references on this kind of tricks include

Siegfried Echterhoff, *Morita Equivalent Twisted Actions and a New Version of the Packer-Raeburn Stabilization Trick*, Journal of the London Mathematical Society **50** Issue 1 (1994) 170–186, doi:10.1112/jlms/50.1.170

and part 5 here:

Noé Bárcenas, *Twisted geometric K-homology for proper actions of discrete groups*, Journal of Topology and Analysis (2018) doi:10.1142/S1793525319500729, arXiv:1501.06050.