A Research Study Investigating How Adults With Overweight or Obesity, With or Without Type 2 Diabetes, Tolerate Switching to a New Treatment (Zenagamtide) From Their Current Semaglutide Medication

Inclusion Criteria: * Male or female (sex assigned at birth, inclusive of all gender identities). * Age 18 years or older at the time of signing the informed consent. * Considered eligible based on the medical history, physical examination, and the results of vital signs, electrocardiogram and clinical laboratory tests performed during the screening visit, as judged by the investigator. * Participants on a stable treatment dose of (subcutaneous) s.c. semaglutide for at least 4 weeks. Only for participants with T2D: * Diagnosed with type 2 diabetes before screening. * Treatment with 0-2 marketed oral glucose-lowering medications (metformin or sodium-glucose cotransporter-2 inhibitors (SGLT2i) as a single agent or in combination) according to local label. Treatment with oral glucose-lowering medications must be stable (same drug(s), stable daily doses) for at least 90 days before screening. Exclusion Criteria: * Female who is pregnant, breast-feeding or intends to become pregnant or is of childbearing potential and not using adequate contraceptive method. * History of reduction in dose of semaglutide, due to intolerability, without successful reescalation. * Presence of any clinically relevant condition that causes symptoms which are similar to the gastrointestinal adverse events (GI AEs) linked to glucagon-like peptide-1 receptor agonist (GLP-1 RA) treatment, and which could confound evaluation of GLP-1 RA-related GI AEs and tolerability endpoints. * Ongoing use of medications causing clinically relevant gastrointestinal symptoms that could confound evaluation of GLP-1 RA-related GI AEs and tolerability endpoints, as judged by the investigator. * Use of prescription medicinal products or non-prescription drugs within 14 days before screening. Exceptions are: * use of s.c. semaglutide as described in inclusion criterion 5 * glucose-lowering medication mentioned in inclusion criterion 7 (only for participants with T2D) * stable use (initiated minimum 30 days before screening) of statins, blood pressure lowering medicine, beta blockers * highly effective contraceptives * occasional use of paracetamol, ibuprofen and acetylsalicylic acid. Only for participants without T2D: \- Presence or history of any clinically relevant respiratory, metabolic, renal, hepatic, cardiovascular, gastrointestinal, or endocrinological conditions. Only for participants with T2D: * Glycated haemoglobin (HbA1c) more than or equal to (≥) 10.5 percent (%) \[91 millimoles per mole (mmol/mol)\] at screening. * Participant with diabetic retinopathy or maculopathy who received treatment with retinal photocoagulation, vitrectomy or anti-Vascular Endothelial Growth Factor (anti-VEGF) within 180 days before screening or are expected to require treatment within 180 days after screening. Diabetic retinopathy or maculopathy must be verified by an eye examination performed within 90 days before screening. Pharmacological pupil-dilation is a requirement unless using a digital fundus photography camera specified for non-dilated examination. * Presence or history of any clinically relevant respiratory, metabolic, renal, hepatic, cardiovascular, gastrointestinal, or endocrinological conditions, except conditions associated with diabetes mellitus.