My house was built in 1921 and when we were stripping the old plaster we found a similar gap and poorly ties in wall, I took out the half bricks in the untied wall and knock 2 bricks out of the main wall then just added a full brick back in the untied wall and filled the gaps left either side of the new brick,
That was 10 years ago at least and nothing has moved.
There must be dozens of clever modern ties you can install, depending on what access you might have to either side. I think you’d be better off with a few modern mechanical ties than trying to reinstall brick ties. Quite a gap there so if it was my house, I’d want some professional advice if only to understand why it has moved so much.
it was normal in olden times to just butt extensions and even walls built at the same time together,
get some stainless threaded bar, drill into the outer wall at an angle every few courses, (forming a V) the bits left inside can be bent into the mortar courses,
if you have resin use it, if not a thin mortar mix will work,
I'm with screwdriver there must be some modern devices to pull it together does Helifix have anything in their range? or possibly some heavy duty wallties. Yes I would seek profesional advice a mate of mine fully qualified structural engineer was called to inspect a house with some 'cracks' he advised immediate evacuation the house was pulled down in the end; there was a stream running under it! it was the lawyers who did best out of that one.
just get it pointed up and plastered. I wouldn't loose sleep over it. it hasn't gone anywhere outside . just have a look in 6 month if it has moved again significantly do something about it . when I bought my house there were cracks all round it on the corners of the house .surveyors quoting sinking founds the full works wanting to dig holes to look costing a grand all that happened was the roof beams had spread and settled . I just re pointed the whole house 30 years ago and nothing has cracked since .its a mountain out of a mole hill
I agree that sort of movement is usually of no consequence. On the other hand it might be an early warning of a floor collapsing or subsiding since the gap is clearly larger at the top. So it's probably nothing but still worth finding out exactly what is moving and where.