Galaxy evolution in compact groups - III. Structural analysis of galaxies and dynamical state of non-isolated compact groups

Compact Groups (CGs) of galaxies are dense systems where projected separations are comparable to their optical diameters. A subset - non-isolated CGs - are embedded within major structures. Using multi-band S-PLUS data, we analyse galaxies in 122 non-isolated CGs within more massive systems such as larger groups and clusters. We compare them to galaxies in the host structures, hereafter surrounding group galaxies. Structural parameters were obtained with MorphoPLUS, a pipeline for multi-wavelength S\'ersic profile fitting. Dividing galaxies into early (ETG), transition, or late types (LTG), we find: (1) Non-isolated CGs host higher quenched fractions and more ETGs, especially for stellar masses $\log(M/M_\odot) > 10.2$, than surrounding groups. (2) S\'ersic indices increase with wavelength for all morphological types in both environments, whereas effective radii show a stronger morphology-dependent behaviour - ETGs become more compact towards redder bands, while LTGs exhibit flatter $Re(\lambda)$ trends. Environmental differences remain weak, with only a modest enhancement of the gradients for ETGs in non-isolated CGs. (3) Transition galaxies in CGs show a concentrated $R_e$-$n$ distribution and faint-end bimodality, consistent with ongoing morphological transformation absent in surrounding groups. (4) Phase-space analysis indicates that some CGs in clusters are projection artefacts, while others are genuine dense systems at various infall stages, from recent arrivals to ancient remnants. These results show that galaxies in non-isolated CGs follow distinct evolutionary paths compared to their surrounding groups galaxies, suggesting that the compact configuration plays a unique role beyond the influence of the larger-scale environment.