That sounds like an fragile setup if you depend on a single email account to get 2FA codes. I have them configured typically on my office workstation (reachable

That sounds like an fragile setup if you depend on a single email account to get 2FA codes. I have them configured typically on my office workstation (reachable remotely if everything works), on my laptop, on my phone, and I have the static backup codes in my password manager which is also distributed over several indpendent machines. Of course if you have to respond to incoming tickets within a guaranteed short timeframe that gets a problem if nothing can come in. Make your risk assessment in advance: Can I live without it for a while, in the worst case even until I have an alternative provider? If so then just do so when an outage happens. If that's not acceptable for your case you need to have an independent backup before the first outage.