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

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 antibiot…