A near-infrared interferometric survey of debris-disk stars. VII. The hot/warm dust connection

(abridged) Context. The origin of hot exozodiacal dust and its connection with outer dust reservoirs remains unclear. Aims. We aim to explore the possible connection between hot exozodiacal dust and warm dust reservoirs (> 100 K) in asteroid belts. Methods. We use precision near-infrared interferometry with VLTI/PIONIER to search for resolved emission at H band around a selected sample of nearby stars. Results. Our observations reveal the presence of resolved near-infrared emission around 17 out of 52 stars, four of which are shown to be due to a previously unknown stellar companion. The 13 other H-band excesses are thought to originate from the thermal emission of hot dust grains. Taking into account earlier PIONIER observations, and after reevaluating the warm dust content of all our PIONIER targets through spectral energy distribution modeling, we find a detection rate of 17.1(+8.1)(-4.6)% for H-band excess around main sequence stars hosting warm dust belts, which is statistically compatible with the occurrence rate of 14.6(+4.3)(-2.8)% found around stars showing no signs of warm dust. After correcting for the sensitivity loss due to partly unresolved hot disks, under the assumption that they are arranged in a thin ring around their sublimation radius, we however find tentative evidence at the 3{\sigma} level that H-band excesses around stars with outer dust reservoirs (warm or cold) could be statistically larger than H-band excesses around stars with no detectable outer dust. Conclusions. Our observations do not suggest a direct connection between warm and hot dust populations, at the sensitivity level of the considered instruments, although they bring to light a possible correlation between the level of H-band excesses and the presence of outer dust reservoirs in general.