After looking into it quite a bit myself, the ones that seem most promising are Mailbox, Posteo, Tuta and Fastmail. I’ve tried all of them except for Mailbox and they’re all pretty solid options.
Each have their selling points, so I would recommend taking a quick look at all of them before deciding. Posteo for example is really cheap unless you need loads of extra aliases and storage, but does not support custom domains. Tuta does not support third party clients. Fastmail is kinda expensive, but gives you more storage than the others and some extra features. Mailbox seems really similar to Posteo to me in a lot of ways, but has more features in their more expensive plans.
Ehh… It has a plugin that lets you run their web client from within Thunderbird. To me that doesn’t really count, but maybe it does for you and all power to you if so.
Edit: Typo