Plex has a name for not transcoding things, it’s called Direct Play, and there are ways it can be disabled, which would cause a transcode.
Plex has a name for videos that are in an acceptable encoding but the wrong container for a player, for example a TV that requires MP4 but you have MKV, that would be adjusted with the feature Plex calls Direct Stream. It just repackages the mkv into an mp4 in that case.
You want your player and server to be setup with words like Original Quality or Automatic or Highest which are the terms used in some of the Plex settings. Another obvious one is the checkbox for Direct Play and the checkbox for Direct Stream. You might need to Settings > Show Advanced to see those two checkboxes.
I once had a user who had accidentally changed his setting away from Original Quality, and all he needed was to put that back.
It’s worth looking at. If you post your logs, we can dive into it more.
