We report on the first integration of novel magnetic microcalorimeter detectors (MMCs), developed within SPARC (Stored Particles Atomic Physics Research Collaboration), into the experimental environment of storage rings at GSI, Darmstadt, namely at the electron cooler of CRYRING@ESR. Two of these detector systems were positioned at the 0° and 180° view ports of the cooler section to obtain high-resolution x-ray spectra originating from a stored beam of hydrogen-like uranium interacting with the cooler electrons. While previous test measurements with microcalorimeters at the accelerator facility of GSI were conducted in the mode of well-established stand-alone operation, for the present experiment we implemented several notable modifications to exploit the full potential of this type of detector for precision x-ray spectroscopy of stored heavy ions. Among these are a new readout system compatible with the multi branch system data acquisition platform of GSI, the synchronization of a quasi-continuous energy calibration with the operation cycle of the accelerator facility, as well as the first exploitation of the maXs detectors' time resolution to apply coincidence conditions for the detection of photons and charge-changed ions.