There is a class of residence (but not work) permits (non lucrativa / non-working / visitor / retiree) for people with stable income sources outside of the country. This kind of residence permit should be perfect for people with remote jobs who want to stay for more than 3 months in a country they like, but don't have relatives or a job there. However, it's hard to find a lot of info on this topic, except for Spain: 1,2.
Judging from those articles, there are plenty of hidden obstacles (like you need to sign the lease before you get the permit; and what to do with it if you're refused?).
Or in Cyprus, you should apply for residence permit ("pink slip") on the place, so it's not clear how you apply for long term visa to get there. And after you apply for a permit, there is a several months waiting period - what if your visa expires? Should you leave or stay?
So, are there countries where it's actually straightforward to get a visa and then a temporary residence permit for a person with remote job or passive income?