More than two years into the COVID-19 pandemic, most of the population has developed anti-SARS-CoV-2 antibodies from infection and/or vaccination. However, public health decision-making is hindered by the lack of up-to-date and precise characterization of the immune landscape in the population. Here, we estimated anti-SARS-CoV-2 antibodies seroprevalence and cross-variant neutralization capacity after Omicron became dominant in Geneva, Switzerland. We conducted a population-based serosurvey between April 29 and June 9, 2022, recruiting children and adults of all ages from age-stratified random samples of the general population of Geneva, Switzerland. We tested for anti-SARS-CoV-2 antibodies using commercial immunoassays targeting either the spike (S) or nucleocapsid (N) protein, and for antibody neutralization capacity against different SARS-CoV-2 variants using a cell-free Spike trimer-ACE2 binding-based surrogate neutralization assay. We estimated seroprevalence and neutralization capacity using a Bayesian modeling framework accounting for the demographics, vaccination, and infection statuses of the Geneva population. Among the 2521 individuals included in the analysis, the estimated total antibodies seroprevalence was 93.8% (95% CrI 93.1-94.5), including 72.4% (70.0-74.7) for infection-induced antibodies. Estimates of neutralizing antibodies in a representative subsample (N=1160) ranged from 79.5% (77.1-81.8) against the Alpha variant to 46.7% (43.0-50.4) against the Omicron BA.4/BA.5 subvariants. Despite having high seroprevalence of infection-induced antibodies (76.7% [69.7-83.0] for ages 0-5 years, 90.5% [86.5-94.1] for ages 6-11 years), children aged <12 years had substantially lower neutralizing activity than older participants, particularly against Omicron subvariants. Overall, vaccination was associated with higher neutralizing activity against pre-Omicron variants. Vaccine booster alongside recent infection was associated with higher neutralizing activity against Omicron subvariants. While most of the Geneva population has developed anti-SARS-CoV-2 antibodies through vaccination and/or infection, less than half has neutralizing activity against the currently circulating Omicron BA.5 subvariant. Hybrid immunity obtained through booster vaccination and infection confers the greatest neutralization capacity, including against Omicron. General Directorate of Health in Geneva canton, Private Foundation of the Geneva University Hospitals, European Commission ("CoVICIS" grant), and a private foundation advised by CARIGEST SA.