Every single one of these tools only connect to Gmail. It's kind of a bummer.
That isn't really a thing though. The email protocols cover the format of the message and how it's transmitted, there isn't any standard for how servers are implemented that would allow one to develop email software that automatically works with any server. Otherwise Nylas wouldn't be a thing.
The fact that clients such as Thunderbird (or mutt) exist and work with basically all email hosts is a testament to this fact.