Deep surveys have helped to unveil the history of past and present galaxy mergers, and, in particular, uncovering their tidal debris and co-located globular clusters (GCs). Euclid's unique combination of capabilities (spatial resolution, depth, and wide sky coverage) will make it a groundbreaking tool for galactic archaeology in the Local Universe, bringing low-surface-brightness (LSB) science into the era of large-scale astronomical surveys. Euclid's Early Release Observations (ERO) demonstrate this potential with a field of view that includes several galaxies in the Dorado group. In this paper, we aim to derive from this image a mass assembly scenario for its main galaxies: NGC,1549, NGC,1553, and NGC,1546. We detected their internal and external diffuse structures, and identified candidate GCs. By analysing the colours and distributions of the diffuse structures and candidate GCs, we can place constraints on the galaxies' mass assembly and merger histories. The results demonstrate that feature morphology, surface brightness, colours, and GC density profiles are consistent with galaxies that have undergone different merger scenarios. We classify NGC,1549 as a pure elliptical galaxy that has undergone a major merger. NGC,1553 appears to have recently transitioned from a late-type galaxy to early type, after a series of radial minor to intermediate mergers. NGC,1546 is a rare specimen of galaxy with an undisturbed disk and a prominent diffuse stellar halo, which we infer has been fed by minor mergers and then disturbed by the tidal effect from NGC,1553. Finally, we identify limitations specific to the observing conditions of this ERO, in particular, stray light in the visible and persistence in the near-infrared bands. Once these issues are addressed and the extended emission from LSB objects is preserved by the data-processing pipeline, the Euclid Wide Survey will allow for studies of the Local Universe to be extended to statistical ensembles over a large part of the extragalactic sky.
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