Recently, a shared hosting company where I had the emails went off-the-grid in a puff. I know I should have taken backups, but, it seems trivial that why would a company just shut off the servers/ stop responding if the service has been impeccable for last 5 years? This is another story.

So, what can I do to just keep a backup of all my emails (one @gmail.com and other personal website emails)?

Maybe for me, just having those emails accessible somewhere is more important (other than primary source/ provider)

Thanks