There is no good way to make that work other than putting a sheet of tempered glass over it. You might try a better layout that doesnt block the fireplace.

Well, the good news would be that there would not be any question of meeting wall combustibility rules for any likely high performance range. But as noted, brick isn't the easiest surface to clean.

If the kitchen were mainly tile and stainless steel everywhere (with a floor drain), one could imagine steam cleaning at regular intervals.

One might imagine re-purposing a pop-up down-draft mechanism to protrude a protective panel; a real hood would be used for actual cooktop ventilation.

If the cooktop is spaced sufficiently from the brick, splatter onto the brick might be minimal. But still, pressure washing or steam lancing would seem to be needed at some possibly extended interval. Perhaps a smooth demi backsplash or gap could be used and wall cleaning drips caught by an array of towels during cleaning.

In the image below from Handcrafted Metal, Inc., one may see that stone was used as a backsplash. It doesn't look coated. But note that there is a decent spacing from cooktop to ledge, then further spacing to the wall.

P.S. A masonry outlet might be able to advise on coatings that are reasonably visually acceptable. I know that matte coatings for concrete exist.

The hood will need a steel duct to the outside, with the blower in the hood, in-line with the duct, or outside. Due to its low temperature (unless you have a grease fire), the duct can run almost anywhere given some modest spacing from combustibles. Runs should be upward as much as possible. Speak with your code enforcement officer for all deviations from common practice.