Mist coat then primer? Or do I just paint?

Usually a mist coat is all that is required- then subsequent coats of emulsion until a satisfactory cover is achieved, however It is possible you may get tar stains permeating through from the original chimney stack. These brown stains will be very obvious and will immediately show through any amount of emulsion. If you notice any brown staining you will need to use a stain blocker.

Why do you think you need a stain blocker? Usual process is to proceed with your top coats now. But thin at least the first coat. Mist coating does not 'seal' the plaster as many say. The plaster is still very porous and its still possible to cause problems by now applying a full coat , and ultimately the finish will be better. Re:patchy. You can always give another mist coat but dilute less mybe 80:20 The main purpose of an initial mist coat is to get some paint soaking into the plaster. Subsequent coats of paint achieve obliteration

Lets hope they pva the soot on the breast be for plastering if not stains from soot will seep through you can try oil base paint gloss let dry and see what happens re paint . kind regards John T

2 mist coats then 2 coats of your final colour should be fine