How do you access these email addresses anyways? I think it's safe to assume you're not paying a G Suite subscription for each of them...
I actually don't access my email from my phone, but the hosting provider (again, pair.com) has a web UI for accessing email (very roughly comparable to gmail) so I certainly could log on there, or could install an IMAP email client on my phone to browse the email until it gets POPped off the host when I am back at the laptop.
When switching laptops, I would restore my local email from a backup (I guess I'm willing to lose a day or three, and try to remember what was important), or rsync the email files back from my fallback/old laptop. I have a somewhat regular routine to upload those files to my pair.com shell account storage (tar, gz, gpg encrypted, then scp, and sometimes to my free google storage and/or AWS glacier), as well as rsyncing key files with a script (which has grown over time to become a full restore for all the accounts I use on my computer) to the old/fallback laptop, and semi-periodic full backups (carefully selected then tar/gz/gpg encrypted) of files that matter, to optical off-site media (not enough volume for tape quite yet I guess).
I tried to answer the access question better in another edit to my original comment above.... Let me know if not.
Instead of doing all that stuff and getting your hands dirty with AWS and .tar .gz etc., would you use a web-based email client where, with one login, you can access to all your email addresses?
Not in an unified inbox, but have them as separates. Say cmd+1 is quickly switching to address #1, cmd +2 is switching to address #2 and so on...
When you'd be switching devices, you'd just log in once and get access to all of them.
Would you use that?
Otherwise (with multi-logins), I could do that with my provider's email web UI in browser tabs (or save the logins in the browser, which I generally do not), for all the ones I designate to them as separate mailboxes (they have some number included, then you pay more after that), or could have a mutt script+window to switch to a different mutt data directory for each.
But I have the other backup stuff largely automated now, so I don't mind much. (Plus it makes me feel good to run scripts I wrote & tested carefully, on my PC.) There would certainly be simpler ways. Maybe I'll reconsider someday if I want to change. :) (Edit: for my own data, I avoid SaaS generally, as I like a sense of control. Same reason I guess that I go to the trouble to learn/use OpenBSD.)
Two killer features are:
1: catch all (office 365 did not have this when I switched away from them in 2014) 2: automatic categorisation which no one else seems to have.
If anyone knows a provider that has these I’d be most interested in hearing about them!