In my old team's case, the shift was 10am-10pm either Mon-Thu or Fri-Sun. If you needed to commute or grab lunch or something, you just had to coordinate with the secondary oncaller to cover for you for a half-hour or whatever.
Stuff like bathroom visits, showers, etc aren't usually a big deal since 1) we didn't get paged that often (see the SRE Book on proper alerting design) and 2) three minutes is longer than you'd think. Usually plenty of time to "wrap things up" and get back to your laptop.
If your internet dropped out, you'd either switch to tethering, get your secondary to cover while you drove to the office or a coffee shop, or worst case contact your manager to help find emergency coverage.
Normally when I was oncall, I'd be on the couch playing video games or watching a movie with my work laptop nearby and logged into a shell on my work desktop.