The real protection is to get your own domain which Fastmail of course supports, so you can point it at a different email provider if worst comes to worst, like ajross's plausible proposition that:
"[...] I'd put the odds of Fastmail failing entirely as a business rather higher that those of any single user having an unresolvable 2FA glitch with a gmail account. In the world of real data and not anecdata, Big Tech is incredibly reliable."