Have you tried cleaning it with TSP? That and a scrub brush should get the soot off. You'll need to rinse well and keep changing the dirty water. If the bricks have a sealer on them, prime with BIN shellac white primer. That will block any left-over soot from coming through. You can paint it any color you like which would be the easiest. If the bricks weren't sealed, you could have applied a limewash. A limewash product seeps into the unsealed brick and cannot be applied over previously sealed brick.

How do you know if the bricks were
sealed? I’ve done several scrubbing with TSP which got a lot of the soot off the bricks but didn’t do a lot in the grout.

You mentioned they were "glazed". Are the bricks shiny?

Yes they are dark rusty red shiny bricks. The house was built in the 60’s,

Then they most likely have a sealer on them. I would scrub the grout with the TSP and paint everything.

Thank you for your help.