Depression screening (with varying forms of intervention) reduces depression symptoms in follow up, and the screening tools are fairly accurate. Suicide screening (with various interventions) does not reduce suicidal ideation or suicide attempts and may actually increase attempts, though the evidence is very limited.
Depression and Suicide Risk Screening: Updated Evidence Report and Systematic Review for the US Preventive Services Task Force. JAMA. 2023 Jun 20;329(23):2068-2085. doi: 10.1001/jama.2023.7787.