A Study to Test Whether Different Doses of BI 1291583 Help People With Bronchiectasis

This study is open to adults with bronchiectasis. People can join the study if they produce sputum and have a history of flare-ups (also called exacerbations). The purpose of this study is to find out whether a medicine called BI 1291583 helps people with bronchiectasis. Participants are put into 4 groups randomly, which means by chance. Participants in groups 1, 2, and 3 get different doses of BI 1291583. Participants in group 4 get placebo. Placebo tablets look like BI 1291583 tablets, but do not contain any medicine. Participants take the tablets once a day. Participants are in the study for between 6 months and 1 year. During this time, they visit the study site about 10 times and get about 5 phone calls from the site staff. The doctors document when participants experience flare-ups during the study. The time to the first flare-ups is compared between the treatment groups. Doctors also regularly check participants' health and take note of any unwanted effects.

Inclusion Criteria: \- Male or female patients: Women of childbearing potential (WOCBP) must be ready and able to use highly effective methods of birth control per ICH M3 (R2) that result in a low failure rate of less than 1% per year when used consistently and correctly, as well as one barrier method. A list of contraception methods meeting these criteria is provided in the patient information. Men participating in this clinical trial must use male contraception (condom or sexual abstinence) if their sexual partner is a WOCBP. * Signed and dated written informed consent prior to admission to the study, in accordance with Good Clinical Practice (GCP) and local legislation. * Age of patients when signing the informed consent ≥18 (for Korea: ≥19) and ≤85 years. * Clinical history consistent with bronchiectasis (e.g., cough, chronic sputum production and/or recurrent respiratory infections) and investigator confirmed diagnosis of bronchiectasis by computed tomography (CT) scan. Subjects whose past chest radiographic image records are not available will undergo a chest CT scan during Screening. Historical scans must not be older than 5 years. * History of pulmonary exacerbations requiring antibiotic treatment. In the 12 months before Visit 1, patients must have had either: * at least 2 exacerbations, or * at least 1 exacerbation and a St. George´s Respiratory Questionnaire (SGRQ) Symptoms score of \>40 at screening visit 1. For patients on stable oral or inhaled antibiotics as chronic treatment for bronchiectasis, at least one exacerbation must have occurred since initiation of stable antibiotics. \- Current sputum producers with a history of chronic expectoration who are able to provide a spontaneous (not induced) sputum sample at Screening Visit 1. Exclusion Criteria: Laboratory and medical examination * Aspartate Aminotransferase (AST) and / or Alanine Aminotransferase (ALT) \>3.0 x upper limit of normal (ULN) at Visit 1, or moderate or severe liver disease (defined by Child-Pugh score B or C hepatic impairment). * Estimated glomerular filtration rate (eGFR) according to Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula \< 30 mL/min at Visit 1. * An absolute blood neutrophil count \