We have an Apex method calling out a REST API Get method, which suddently started responding with binary data instead of JSON. We have not made any changes to the code in the REST API, and using tools like Postman, browser request or JS-fetch returns the appropriate JSON response.
Has anyone experience an issue like this? Other REST APIs do not have the same issue, but our prod, sandbox and scratch orgs all return the same corrupted response.
Here is a sample of the basic call we have in Apex:

@AuraEnabled
  public static String getEventById(String eventId) {
    Http http = new Http();
    HttpRequest request = new HttpRequest();
    request.setEndpoint('https://RESTURI/' + eventId);
    request.setMethod('GET');
    request.setHeader('Content-Type', 'application/json');
    HttpResponse response = http.send(request);
    // Parse the JSON response
    if (response.getStatusCode() != 200) {
      System.debug('The status code returned was not expected: ' + response.getStatusCode() + ' ' + response.getStatus());
      return null;
    }
    return response.getBody();
  }

We are getting a status code 200, but the body of the response is just a lot of random binary data.