I'd really recommend you take another look at Mutt, or Alpine if you're more into pico/nano than vim as editors. It's the best tool I can think of for dealing with large quantities of mail.
* Notifications can be configured to do pretty much whatever you want (by invoking a command when new mail arrives)
* Multi-account support works well (currently have it hooked up to my personal and work accounts simultaneously)
* Developed by a community
* The visual component of HTML mail is irrelevant 99% of the time. A reasonable textual interpretation can be generated by piping the message through `w3m --dump`, a process which can happen automatically inside mutt when viewing those messages with no action required on your part. If you absolutely must see the formatted message with images and such, this is only a keystroke away.
There's a lot of initial configuration to do, granted, but you only need to do it once. Then you stick your mutt directory up on github or similar, and never need to do it again. Setting up a new or different machine is a clone away.
You can learn the initial keybinds in a couple hours (it's a lot simpler than vim), and I think you'll be blown away once you get proficient at it.
This may be a bit extreme, but after many years, I think all GUI mail clients suck. Email is primarily a textual medium at the end of the day.
That, and Mutt's the only thing I can think of where the expected features of a mail client work with reliability. Putting up with Thunderbird's speed/stability or Outlook's stability/searching isn't something we should have to do in 2019.