As shown in sloped ceiling installation video, you cut the planks for the recessed lights as you install the planks, not afterwards.

What is the material underneath the furring strips?

How much space will you have above the planks for the recessed lights? Recessed fixtures for sloped ceilings can be much deeper than those for flat ceilings. For example, this Halo 6 in. Integrated LED White Recessed Light, Sloped Ceiling Trim is six inches deep.

agree, wire and set housings first. one thing to add: lay out the plank direction and seams on paper before the electrician cuts anything, so cans land centered in a board and not right on a seam. also plan any fan or ridge fixture boxes at the same time and add blocking where needed. vaulted ceilings can hide framing surprises, so have a licensed electrician check joist spacing and the insulation contact rating before you buy lights.

If you select real downlights that have removeable bulbs, for sloped ceilings, they have to be recessed first. And they need to match the angle of the ceiling. This is a project for an electrician.

The right-hand recessed housing shown above is for new construction. It cannot be used for your project.

How about you show the vaulted room and the material? If you are trying to light a space , mostly from the ceiling? Call it lighting fail. Lighting is layers, and I'd bet a grand you are lacking lamps and other possibilities.

What exactly from below and show your room....

Recessed lights in vaulted ceilings (or any ceilings for that matter) in living areas are not a great choice. The light is harsh and glaring. Agree with Jan, other forms of lighting are much more aesthetically pleasing and make the room more inviting than downlights in the ceiling. Table lamps, floor lamps, sconces, uplighting are some options.

Personal preference. I like the well-spaced recessed lighting (with dimmer switches) in my vaulted rooms. The dimmed lighting gives a soft overall light to the room when entertaining. Table and floor lamps add the task lighting. Without recessed lights on dimmers, I find the top half of the room to be too dim. The rooms are too big to use chandeliers in lieu of recessed lights and I don’t like rope lighting or other uplighting near the ceiling.

My family room has a cathedral ceiling. When it was built they added recessed ceiling lights, which never get turned on unless we’re looking for a lost earring or something like that. Up lights on beams illuminate the top half of the room and sconces, table lamps and floor lamps complete the picture.