Narrow transient emission lines (flash-ionization features) in early supernova (SN) spectra trace the presence of circumstellar material (CSM) around the massive progenitor stars of core-collapse SNe. The lines disappear within days after the SN explosion, suggesting that this material is spatially confined, and originates from enhanced mass loss shortly (months to a few years) prior to the explosion. We performed a systematic survey of H-rich (Type II) SNe discovered within less than 2 days from the explosion during the first phase of the Zwicky Transient Facility survey (2018-2020), finding 30 events for which a first spectrum was obtained within <2 days from the explosion. The measured fraction of events showing flash-ionization features (>36% at the 95% confidence level) confirms that elevated mass loss in massive stars prior to SN explosion is common. We find that SNe II showing flash-ionization features are not significantly brighter, nor bluer, nor more slowly rising than those without. This implies that CSM interaction does not contribute significantly to their early continuum emission, and that the CSM is likely optically thin. We measured the persistence duration of flash-ionization emission and find that most SNe show flash features for ≈5 days. Rarer events, with persistence timescales >10 days, are brighter and rise longer, suggesting these may be intermediate between regular SNe II and strongly interacting SNe IIn.