The Neutron Star Low-Mass X-ray Binary Swift J1749.4-2807 is the only known eclipsing Accreting Millisecond X-ray Pulsar. On March 2021, the source underwent a short (11-days) and relatively faint outburst, reaching a X-ray luminosity at the peak of only 2×1036 erg s−1. We present the first ever broadband spectral characterization of the system throughout the whole outburst, analyzing 11 NICER observations and XMM-Newton and NuSTAR single observations. This is also one of the very few times that, thanks to NICER, we had the opportunity to follow an X-ray binary outburst in its entirety in the soft X-ray band. According to our analysis, no direct emission from the disc was found (perhaps due to it being too cool), and the the broadband spectrum is well-modelled with a black body component, most likely emitted by a hot spot on the Neutron Star surface, and a Comptonization spectrum arising from a hot electron corona. A moderate truncation radius for the disc, i.e. at ∼20-30 R𝐺, was obtained from the analysis of the smeared profile of the Fe line in the reflection component. The significant detection of a blue-shifted Fe XXVI absorption line at ∼7 keV indicates weakly relativistic disk winds. The discovery of such outflows, typically observed in the soft state of X-ray binaries, is unexpected as the spectral properties of the systems are consistent with a hard-intermediate state. This finding could in principle suggest magnetic propeller-driven winds. In the last few years, a pattern of winds in AMXPs out of the canonical soft states seems to have emerged. However, such detections are typically unconstrained and/or weakly significant, as AMXPs display generally faint outbursts when compared to the other X-ray binaries, due to the state-of-the-art technology. With Athena we will be not only to confirm the existence of such outflows, but to investigate their origin.