  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 non-thermal emission. Further, to better constrain the thermodynamic
structure of the cluster, we complement our analysis with re-processed 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 X-ray hardness distribution. The EMU radio
observations reveal a diffuse radio structure ~400 kpc in projected extent
along the north-west/south-east direction, indicative of strong activity from
the active galactic nucleus within the brightest cluster galaxy. Interestingly,
albeit on a smaller scale, a putative optical star-forming filamentary
structure detected in the HST image is in an excellent alignment with the radio
structure.
