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Only two ultra-diffuse galaxies (UDGs) have spatially resolved stellar population properties, showing flat to rising metallicity profiles, indicative of a different formation pathway than most dwarf galaxies. The scarcity of other low-surface-brightness (LSB) dwarfs with a similar analysis prevents a deeper understanding of this behaviour. We investigated the radial profiles of the ages, metallicities, and star formation histories of four globular cluster (GC)-rich LSB dwarfs, newly observed as part of the ‘Analysis of Galaxies At The Extremes’ (AGATE) collaboration. DFX1 and DF07 are bona fide UDGs, while PUDG-R27 and VCC 1448 are ‘nearly UDGs’. Comparing their and DF44’s properties to simulations, we aim to reveal their formation pathways. We used the full-spectral-fitting code pPXF to fit different spectra extracted in annular apertures in a bid to recover the stellar population properties and compute their gradients. We compared these results with a sample of literature classical dwarfs and simulations, in particular simulated UDGs. Our five LSB dwarfs have flat age and flat to rising metallicity profiles. Such age gradients are compatible with those of classical dwarfs (observed and from cosmological simulations), but the metallicity gradient diverges. All of our LSB dwarfs (except for PUDG-R27, which shows a pronounced increasing metallicity) are compatible with being on the extreme tail of the age–metallicity gradient relation, suggesting a coeval formation, forming the galaxy all at once. This sample of GC-rich LSB dwarfs with spatially resolved properties provides further evidence that they follow a different formation path than classical dwarfs. However, larger samples with higher-S/N spectra and varying amounts of GC richness are required to set robust constraints on the formation pathways of LSB dwarf galaxies.