So, if I read this correctly, when you try to access Steam or your website using your phone or laptop while both are connected to the internet through your home internet connection, you get DNS errors?
This has nothing to do with GOS, but I'll try to help troubleshoot.
Try:
Do you have any ad-blockers, pi hole, VPN, proxy or Tor services running on your phone, laptop, home router or home network? Try disabling them temporarily.
Log into your home router and it will probably have some diagnostics tools like ping , traceroute and dns resolve (most rioters do). Try doing a name resolution to your website from there.
Also, try connecting to your tutoring website by IP address and not host name. Use https://8.8.8.8/ or 1.1.1.1 (Google & cloudflare dns resolvers) to get the IP (eg, instead of browsing to https://my-tutoring-site.com/index.html navigate to http://#.#.#.#/index.html where #.#.#.# is the ip) just to confirm connectivity
Restart your router
There are too many things to that could cause this, so let's start with the low hanging fruit.