They do? I can’t remember him having any interaction with the council since Changes. Besides chatting with Rashid, have I forgotten something?
Sidhe thinking. Since when can you get rid of an obligation or debt just by taking up another one? Medieval thinking. If you have fiefs in two kingdoms you have to serve two kings and figuring out how to do so is your problem.
The idea that you can have only one nationality, master, etc. is relatively modern and even now far from universally accepted. My wife has two passports, no problem at all.
Mab takes these obligations very seriously. Lea mentoring Molly and helping her protecting Chicago as the ragged lady showed that as well.
There may be conflicts but Mab will not on purpose prevent Harry from his obligations. Worst case that would mean Mab would have to fulfill them in some way.
Everything points to the council having a similar way of thinking. Harry is not the first wizard making deals outside the council and they just claim all wizards regardless of their other obligations.
Besides, they are paying his salary.