No studs just furring strips on brick for cabinet install
Cut horizontal areas behind your wall cabinets for new 2X4 or 2x6 nailers set at the tops of the wall cabinets so they are in line with the screw rail of the new cabinets. Cut out the firring strips too. Cut the where the ends of the 2x will be an inch or two behind the edges of the cabinet, so if the wall paint chips or paper tears, it will not show.

When you cut out the wall, the 2X material should be very near the thickness of both the firring strips and drywall, 1/2" drywall plus 3/4" firring strips, should mean you will need to thin down the 2X material a bit. A table saw can do that with care.

To install the 2X, you can use flat head expansion anchors and construction adhesive





Place an anchor on each end and through the rest of the length of the 2X, about 8-12" apart. Place a few large beads of construction adhesive on the back of the 2X after you drill all the holes in the 2X, but before you drill the brick. It is important to get the anchors in the brick, not the joints, although the horizontal  joints (bed joints) may work, surly the short vertical joints (head joints) you need to stay away from. If the brick is a "core brick" a term used for brick with holes in the inside, do not place any anchors in the middle of the brick, only near the ends. If you know them to be solid brick, then it will not matter.

After the blocking is in place, secure the cabinets with what should take 2" screws, if your cabinets are made with 1/4" backs and 3/4" screw rails and 1" to go into the new blocking you just added. Ideally the screws could be 2 1/4" but typically are not available in that length. 2 1/2" screws could work, but you are taking the chance that the point would "bottom out" on the brick surface before the screws drew the cabinets tight to the wall. I have had screw points dig into the brick a bit before they started shoving the strip off the wall, but that is the chance you would be taking. IMO, not worth the chance....