As someone who is increasingly concerned about the possible outcomes of No Deal Brexit, I would like to ensure that I have some access to funds and banking services outside the EU that's as convenient as possible without depending on any UK treaty arrangement, mutual recognition, functioning UK bank services or telephony, etc.
I believe that most bank accounts come with residency requirements. Is there an EU-based bank that offers Euro bank accounts to non-resident non-EU nationals? Ideally that will accept an online application? (Estonia?)