Context. The Solar Orbiter spacecraft made its first close perihelion passes in 2022, reaching 0.32 au on 26 March and 0.29 au on 12 October. Transient activity was relatively low, making it possible to perform measurements of the quiet-time suprathermal ion pool over multi-day periods. Aims. The inner heliosphere suprathermal ion pool is a source of seed particles accelerated by coronal mass ejection-driven shocks. Determining its constituents and their dependence on solar activity, location, and time is therefore critical to building physical models of particle acceleration from solar events. Methods. By selecting low-activity periods on Solar Orbiter during perihelia passes, and comparing them with a nearly identical monitoring instrument at 1 au, the observed differences in intensities can be related to factors such as distance from the Sun, transient events, and interacting solar wind streams. Results. Below ∼1 MeV/nucleon, the observed quiet-time spectra at 0.32 au for H, ⁴He, ³He, and Fe rise toward low energies, as observed previously during longer periods at 1 au, and they show a heavy ion composition that has markers of impulsive solar flare material, such as relatively high ³He:⁴He, and a high Fe/O ratio. The proton and helium abundances are much higher, consistent with a source in corotating interaction regions. Surveying all semi-quiet times during the mission, there is only a modest (∼15%) increase in the fluences in the inner heliosphere compared to 1 au, indicating small gradients in these populations between 1 and 0.3 au.