Hi! We had a discussion with Microsoft about this.
Azure Data Factory behaviour is RFC-compliant behaviour. RFC-standard defines that relative url's SHOULD NOT start with / -character. Using / -character will cause the path to be assumed as absolute path to the domain. Standard here: https://datatracker.ietf.org/doc/html/rfc1808#section-5
So, if a REST API says it is returning a relative URL but it starts with /, this is wrong behaviour and the API should be fixed to follow standards.
Now, the question becomes that whether Data Factory allows manipulation of values retrieved from the body of a response (when reading the nextPageUrl for example, can we manipulate that before the activity uses it for pagination), if a API is not following standard behaviour. This is not currently possible, this was confirmed with the product team.
So Steven in your situation, if possible, use relative url without the leading /-character. If you are reading it from the initial requests' body, so you have no control over the value that is attempted to used dynamically in the pagination logic, then you have to request a change from the team owning the API.