SPT-CL J2106-5844 is among the most massive galaxy clusters at z>1 yet discovered. While initially used in cosmological tests to assess the compatibility with $Lambda$CDM cosmology of such a massive virialized object at this redshift, more recent studies indicate SPT-CL J2106-5844 is undergoing a major merger, and is not an isolated system with a singular, well-defined halo. We use sensitive, high spatial resolution measurements from ALMA and ACA of the thermal SZ effect to reconstruct the pressure distribution of the intracluster medium in this system. These measurements are coupled with radio observations from the EMU pilot survey, using ASKAP and the ATCA to search for diffuse nonthermal emission. Further, to better constrain the thermodynamic structure of the cluster, we complement our analysis with reprocessed archival $Chandra$ observations. We fit the ALMA+ACA SZ data in $uv$-space using a Bayesian forward modelling technique. The ASKAP and ATCA data are processed and imaged to specifically highlight any potential diffuse radio emission. In the ALMA+ACA SZ data, we reliably identify at high significance two main gas components associated with the mass clumps inferred from weak lensing. Our statistical test excludes at the ~9.9$sigma$ level the possibility of describing the system with a single SZ component. While the components had been more difficult to identify in the X-ray data alone, we find that the bimodal gas distribution is supported by the X-ray hardness distribution. The EMU radio observations reveal a diffuse radio structure ~400 kpc in projected extent along the northwest-southeast direction, indicative of strong activity from the active galactic nucleus within the brightest cluster galaxy. Interestingly, a putative optical star-forming filamentary structure detected in the HST image is in an excellent alignment with the radio structure, albeit on a smaller scale.
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