One problem: He charges it overnight and now every morning he has to reboot his router in order to have access to the internet. He did not have to do this before the watch came along.
I’d have to vote for a coincidence. It “should” be easy to eliminate the watch as the problem, since it happens ever night. Charge the watch during the day for a while and see if the system still needs a morning reboot.
My first thought is the router or modem is the culprit.
Something else is interfering with his wireless router. Could be a small power surge or more than likely the modem itself. Is his router an all-in-one combo or an individual modem and wireless setup?
all routers even SOHO gear have some type of logging on them. I’d say pull the logs or have it log to something else (syslog-ng on a Pi for instance) and see what’s going on. It’s unlikely that the watch, or any single host is the issue. The easies way to eliminate it, is to just turn the watch off tonight and see how the router reacts in the morning. If the problem persists, it’s not the watch. Syslog is going to be the key to identifying the actual root issue.
When I had Comcast cable service, I went through periods of periodic service drops on a daily basis. It always appeared to be a router issue, and Xfinity replaced the router a couple of times. But the problem persisted. Eventually a Comcast tech found that a device a block away on their service line had a weak seal and was invaded by ants. So, even the router might be a red herring.