Tableau Server returned an error at request. Tableau Server server code: 401001

When publishing to Tableau Server, you get the following error:

Tableau Server returned an error at request. Tableau Server server code: 401001
Exception:
Tableau.Api.Exceptions.TableauRequestException: A Tableau Server exception occured. HTTP Status Code: 401, Internal Code: 401001

This may either indicate an incorrect site or project name (site and project name is case sensitive!) or a login error: The Tableau REST API requires passwords containing certain characters to be escaped -- however, if a password contains more than one escaped character, the request will be denied.

This is described here:

https://community.tableau.com/s/question/0D54T000006B4KLSA0/tableau-server-rest-api-login-problems-escaping-passwords-with-special-characters