Is it ethical to take external consultancy jobs during a fully funded PhD programme? I am on a three year PhD programme which is fully funded. My salary is fair, nothing flashy but definitely enough to get by without having to do anything else.

Recently, I was offered to start a new course and teach it at a different university from the one where I am employed, in exchange for an extra salary. I am very inclined to say yes to this because it is a really good opportunity to gain teaching experience, promote my research center and earn more money.

From a bit of Googling around it seems that there are different takes on this depending on the country, but that the general approach is that bijobs during the PhD is totally fine. My university (a Scandinavian one), however, officially states that applicants to PhD programs cannot have other jobs. It's confusing to me and I'm not comfortable just naively considering it consultancy work rather than an actual job, and playing stupid if bureaucracy catches up.

My supervisor has a very "long leash" advising style so his opinion on the matter is that I should do whatever I'm comfortable with as long as I'm fulfilling my academic duties. I'm pretty comfortable with it, but the rules are fuzzy and what I really want is some examples of what other people have done in this situation.
Some universities have policies against funded PhD students doing other paid work. You may want to consult the dean's office (or the equivalent authority at your institution) about this before you sign a contract for a second job (albeit temporary), since there may be serious repercussions such as the termination of your funding.

Your funding may also be coming from a grant which somehow prohibits another income source. This can be unbeknownst to you, arranged by your professor or school, which may be strange and perhaps even unethical, but not impossible and not unheard of. I have seen more than one grant agreement where an "obligation of the researcher to work exclusively for the project" is explicitly stated.

Thus, before you accept the job, make sure to ask your advisor and your dean if there are any conditions which would prohibit you from doing so. You don't have to be very specific about the offer you received. I would say you don't have to hide the facts either, but there are many flavors of advisors and deans so I won't comment further on how you communicate with them. Just make sure to ask.