A Research Study to Investigate the Effects of CagriSema Compared to Placebo in People With Type 2 Diabetes and Painful Diabetic Peripheral Neuropathy

Key Inclusion Criteria: * Male or female. * Age 18 years or above at the time of signing the informed consent. * Body mass index (BMI) ≥25.0 kilogram per square meter (kg/m\^2) at screening. * Diagnosis of type 2 diabetes (T2D) ≥180 days before screening. \-- For participants on anti-diabetic drugs: Stable daily and/or weekly dose(s) ≥90 days before screening of any of the following anti-diabetic drug(s) or combination regimen(s) at effective or maximum tolerated dose, as judged by the investigator: * Treatment with 1-3 marketed oral anti-diabetic drugs (OADs) (metformin, α-glucosidase inhibitors (AGI), glinides, sodium-glucose co-transporter 2 inhibitors (SGLT2i), thiazolidinediones, or sulphonylureas (SU) as a single agent or in combination) according to local guidelines. * Treatment with basal or basal-bolus insulin (including premixed insulin formulations) according to local guidelines. * HbA1c ≤10.5 % (91 millimole per mole \[mmol/mol\]) and ≥6.0 % (42 mmol/mol), as determined by central laboratory at screening. * Diagnosis of painful diabetic peripheral neuropathy (pDPN) at screening as well as at the following criteria: \-- Participant with self-reported pain consistent with pDPN for a minimum of 3 months before screening, as judged by the investigator. * Stable pharmacological and non-pharmacological treatment of pain for a minimum of 3 months before screening, in the opinion of the investigator. The treatment regimen should adhere to local guidelines (if available). Key Exclusion Criteria: * Female who is pregnant, breast-feeding or intends to become pregnant or is of childbearing potential and not using a highly effective contraceptive method. * Use of any glucagon-like peptide-1 receptor agonist (GLP-1 RA), including medication with GLP-1 RA activity, (DPP-4), or amylin analogue within 60 days before screening. * Significant use of opioids, cannabinoids or benzodiazepines within 30 days before screening, in the opinion of the investigator. Significant use is defined as use that renders it unlikely that the participant is able to comply with protocol requirements for discouraged medications. * Anticipated initiation or clinically relevant change in concomitant medications (for more than 14 consecutive days during the study) known to affect weight or glucose metabolism (e.g., orlistat, thyroid hormones or oral corticosteroids). * Planned initiation or change in anti-depressant, anti-psychotic or anti-epileptic medication. If participants are already taking such medication, they should have stable and optimised treatment for at least 8 weeks before screening. * Presence or history of epilepsy and fibromyalgia. * Presence of non-diabetic neuropathies, in the opinion of the investigator. * Uncontrolled and potentially unstable diabetic retinopathy or maculopathy. Verified by a fundus examination and OCT assessment performed within 90 days before screening or in the period between screening and randomisation. Pharmacological pupil-dilation is a requirement unless using a digital fundus photography camera specified for non-dilated examination. * Any other painful medical condition(s) where the pain is significantly more severe than the diabetic peripheral neuropathy pain, as judged by the investigator (participants will not be excluded if the pain is transient in nature). * History of suicidal attempt within 5 years before screening * Suicidal behaviour within 1 month before screening. * Renal impairment with estimated Glomerular Filtration Rate (eGFR) \<30 ml/min/1.73 m2 as determined by central laboratory at screening. * Exposure to an investigational medicinal product within 90 days or 5 half-lives of the investigational medicinal product (if known), whichever is longer, before screening.