Spend almost an hour to try to understand why Tusky doesn't work with this instance and Android 7.0. Turns out it is described in the github issue[1], there is an Android issue[2] for it and there pretty much nothing that can be done about it. It's just that Android 7.0 doesn't bother to support a particular elliptic curve HT has in its certificate.

Geez.
[1] https://github.com/Vavassor/Tusky/issues/46
[2] https://code.google.com/p/android/issues/detail?id=224438

I feel sad.

Android 7.1, if you happen to get it any time soon, will fix that. So that's that.