If it is damp there are several ways in, cracked haunching is possible – the mortar hump around the base of the chimney pot. Rain could potentially run down the outside of the liner.
Was the haunch done same time as pointing?
Chimney has a chinamans hat on, which is good but they can corrode surprisingly quickly and perforate. However that would allow water into the liner, which would then enter the stove, not reach the wall. So less likely, and the stove would be wet inside
It looks like a pot hanging cowl which means water can’t realistically get under the cowl and into the masonry flue under the lip, as liner and cowl are joined. I have seen incorrectly installed cowls where water could just get in, but it’s really unlikely and would mean cowl and liner weren’t connected
Was the wall painted previously, or papered? Ie could there have historically been a damp patch there which was masked, and then a change of decor revealed it?
Personally I’d ask the painter guy what he thinks, no finger pointing. And ask him what would be the best thing to do.
Incidentally, have you looked behind the coffin to see what the wall is like there?