I looked into this a bit a year or two ago, and wasn't happy with the alternatives. The main issue for me is that I never delete anything, and so I have nearly 500GB of email, dating back over 20 years (sadly I've lost earlier email due to the cost of even local storage back in those days). I don't want to deal with the data in any way, sorting through it, splitting it up, etc. I just want to dump it all into an email account and have it forever. Many of the alternatives that offer good privacy top out at 20GB or so for their most expensive plan (or less).
Tutanota was the one service I found that let you add (IIRC) arbitrary amounts of storage to your plan, but I found their web interface to be kinda clunky, and let the account expire. I keep wanting to look into this again, but never get around to it.
OneDrive is pretty damn cheap _and_ comes with access to Office on the web. 1tb per family member, with Office? Goodly.
There's no official Linux client, but there are open source ones that perform well.
You could drop your mbox onto a OneDrive sync and then use fetchmail or similar to rip it out of your provider. Each email could be individually encrypted, so you won't have to deal with a 500gb blob to sync.
I'm surprised Outlook held up. In my experience the program starts crapping itself after the first 3-4GiB of emails, and it only gets worse after that. I wouldn't rely on the file remaining intact for long with such a setup...
I remember services available 5+ years ago that would help you with this kind of thing (scanning through email archives by sender), but the ones I remember have all morphed into "tame your inbox" apps, which doesn't solve the same problem.
Tutanota was the one service I found that let you add (IIRC) arbitrary amounts of storage to your plan, but I found their web interface to be kinda clunky, and let the account expire. I keep wanting to look into this again, but never get around to it.