So the shutter speed for f5.6 (with the extender) and f8 (the real f8 without the extender) is the same which suggests to me that the f5.6 in the first photo with the extender is infact f8 even though it's reading f5.6.
Yes.
But this is absolutely straight forward - with the lens fully open, the linear aperture is obviously unchanged, so the extender must change the f ratio by the same amount as it changes the focal length (since the f ratio is simply the focal length divided by the linear aperture).
What the electronics are fooled into saying is irrelevant - so long as you're using TTL metering. If you're using external metering, you'd better know what the actual f-number is ... this is where one of those old fashioned aperture setting rings comes in handy, even though you do have to do a bit of simple mental arithmetic, there's never any doubt as to what size hole you have set ... and personally I find it a lot less confusing than using those multi mode dials.