The issue related to your CR3 files and Drone files are different.
First, Photo Mechanic and Bridge are not the same program and offer different functionality. Bridge takes the raw data and renders it through Adobe's rendering engine to provide you with a viewable image. Photo Mechanic, on the other hand, views the JPEG embedded in your raw file and shows you that, so just because Bridge shows you a full-sized image does not mean that Photo Mechanic will as well.
Your email to our support desk indicated that you are using a very early build of Photo Mechanic (build 2725). While most CR3 files do contain a full-sized embedded JPEG, early builds of Photo Mechanic were unable to find the largest one and instead found a smaller embedded JPEG that was sized at 1620x1080. Update to the latest build of Photo Mechanic and it should resolve the issue with your CR3 files.
With regards to the files from your Drone, most RAW files I have seen from drones do only include a small embedded Preview, and unfortunately without any further action or changes to your settings, this is the best that Photo Mechanic is going to be able to show you. Your options to get a full-sized image in Photo Mechanic are to shoot RAW+JPEG with the drone, use Adobe DNG converter to create a new DNG file from the original DNG that does contain a full-sized preview, or to
enable RAW Rendering (we don't recommend using this option because it is slow and it renders all images on the Contact Sheet, which you won't need for almost any other kind of RAW file since most do contain full-sized previews.