This looks really cool and more modern than Nextcloud. From the homepage, I was a little wary of the idea of hosting my own email server -- doesn't that require a ton of effort due to spam? Or can I use it with an external provider and use this as webmail?

yes, I should make this clearer: You do not actually host the email, tinycld uses a transactional host for sending and receiving. I also have a lot of scars from doing that in the past and I'm happy to pay someone else a few $$ a month for that service.

We support postmark right now (it has spam filtering), mailgun in the near future. Plus probably a pure smtp server for those who _really_ want to do it all themselves.