From a plex perspective, there could be the chance you are transcoding. On your local network, you are probably Direct Playing on your client devices. This is seen by the dashboard on your computer’s Plex app. But normally when a remote user accesses Plex, it is likely to start a transcode. This could be due to a number of reasons but most of the time it will be because the bandwidth isn’t enough to allow Direct Play. Transcoding can give your CPU a workout, especially if you are software transcoding. You will need a Plex Pass for hardware transcoding which uses less CPU overall.
Used Watchtower on my Synology for a while and it worked well. No issues in that time.
Now I’ve moved to a Nuc and am more experienced with Docker and understand a lot more of it but by no means am a professional by any means, I would say that I wouldn’t use Watchtower. I can definitely see it messing a config up and prefer not to deal with the headache of troubleshooting something without knowing it was an auto update. If I had the time, I may tag the apps I’m happy to auto-update but for now I prefer to have the higher availability.