If you do decide to paint it, ask the experts if you should coat the brick with a product like “Kilz” which is a coating/primer which would prevent any old dirt/ash from seeping through the paint. This is used in areas prone to grease and so forth.
We’ve done it and it looks much better. Our brick was the type with those tiny grooves from the 30’s. Cleaned it well with something called TSP or THP (not STP or THC) or something like that (comes in a powder, mixes with water) and a wire brush. That took a while but it got rid of any loose material, soot, etc. Then a really good primer (2 coats) then 3 coats of paint. We used latex I think (to be honest my wife pretty well did the whole thing). The key was putting so many coats on. No brick or dark tint shows through and it looks 100% better. Sure its non-reversable but if we want red brick again, we can paint it red again.
We’ve done quite a few old brick walls and fireplaces. I’m always surprised by how good it looks because I prefer the look of sealed stone or brick. But, the customer gets what the customer wants.
The key is cleaning and the right type of primer. Go to a real paint store and describe for them exactly what material it is. Home Depot type places usually won’t have it. Sorry I didn’t look at this thread til now, but it seems like it ended up well for you.