ALMA high-resolution surveys have so far focused mainly on large, bright protoplanetary disks, where substructures are routinely detected, leaving compact disks poorly characterized. Yet, the survival of millimeter emission in Class II sources implies that radial drift must have been halted by pressure traps, previously undetected due to limited angular resolution. We present ALMA Band 7 (0.9 mm) continuum observations of 11 of the smallest (R₆₈ < 10 au) Class II disks in Lupus, reaching 0.02'' (2 au) resolution, the highest currently available with ALMA at this wavelength. We detect substructures in 4 disks, including a clear inner cavity of radius 1.6 au, and hints of substructure in 3 more. Two disks also host faint outer rings beyond their bright inner core. Combining these results with demographic information on Class II disks observed with ALMA, we examine how the substructure detection rate varies with disk size, restricting to disks whose diameter is resolved by at least 3 resolution elements. We find that nearly all disks (≳95%) larger than 30 au show substructures, compared to a still substantial ∼50% between 3 and 30 au, with the lower rate likely affected by optical depth. The planet masses required to open gaps within 5 au fall in the super-Earth to mini-Neptune regime. These results demonstrate that substructures are ubiquitous across the disk population, and that planet formation conditions can be probed down to a few au from the host star.