What are our options to update this brick facade?
Your cheapest route would be to paint it by far. If you want to change the texture of the wall, have it stuccoed. That can be done in 2 ways, a 3 coat system with a cement based finish or the 3rd coat can be a latex based product that is normally used in EIFS, (exterior insulated finishing system) The color is part of the finish coat with either system.

The top row of brick will need to be removed to tie the stucco in under the siding edge, leaving the brick there will create a water trap and allow water to get behind the brick. This system is around 3/4" to 1" thick. It can be thicker, sometimes thinner, but I would not let anybody try it.