Re: "page for all 500s": there's a world of difference between "page me with a critical alert at 3am" and "notify me on Monday morning when my normal workday starts". At the extremes:
If my DB health check endpoint is returning 500s for N consecutive checks over M minutes, yeah, please wake me up at 3am!
If one user hit a weird edge case in form validation and got a one-off 500, please don't! We can fix that on Monday.
Not always easy to distinguish those clearly or configure those business hours rules, but for my team at https://heyoncall.com/ that is the goal -- otherwise your team burns out fast. Waking up someone at 3am has a real cost, so you better be sure it's worth it.
Shouldn't Github be large enough to not have anyone on-call, but just rotate the responsible team around the world?