It's definately metal/weld type material I tried to grind it back to get the post down with limited success, hence my welding guess, It's not rust tho the bottom of the tube IS more muck type!
2nd pic shows it best but not perfectly it definitely restricts the diameter less than the sleeves even.
My advice would be to take it to a decent bike shop and ask them what they think the white stuff is and what the explanation could be.
I find it a puzzle. On the one hand, it looks as though the tube has only been reamed down to just above the white bubbles - in which case it needs to be fully reamed anyway. On the other hand, that may be just a coincidence. But what surely can't be a coincidence is if the white bubbling is at exactly the same depth as the bulging on the outside. And if the pin hole on the outside of the seat tube is exactly where there is a white bubble inside.
One possibility is that this is nothing to do with a crack, but there have been one or more small rust holes that have been repaired. It isn't impossible for rust to form underneath a paint blister and go right through the tube before it becomes apparent. If such a hole was small and there was no spread, a decision could quite properly have been taken that it didn't affect the structural integrity of the tube. In that case, it might have been filled with braze and repainted, on the basis that it was perfectly sound.
What doesn't make sense is for it not to have been deeply reamed. If I had that kind of repair, I would want a long seat post going as far down the tube as possible, well past the repair, so as to minimise the strain on the repair. As it stands at present, the strain on the repair is maximised. Looking on the bright side, perhaps it demonstrates the repairer's confidence in his work?
I know it sounds a bit dodgy, but people often drill things deliberately, to save weight.
Still, it's hard to judge from a photo (however good!), so this is just conjecture really. I feel sure an experienced bike shop proprietor would have seen something like this in the past.