As previously said, this is a very common rot fungus, it is feeding on dead wood. You'll have to look at the tree to decide whether the rot is localised or widespread, if the former you may be able to cut it out. By the time it gets to fruiting like this it has been feasting on dead wood for a while, so I would doubt that this is caused by the action of the pruning earlier in the same year, the tree must have already been compromised. The tree surgeon should have noticed this, though he probably preferred to be paid for doing what he had been asked to do rather than tell you that the tree was on its way out and would perhaps be better be removed entirely. Some trees, of course, are happy to rot out their centre and carry on living as a hollow shell, including some fruit trees, though that tends to be trees with a large trunk, and productivity will be compromised.

I would say it is unlikely to be a threat to other healthy trees in your garden: it is extremely common, you'll find it everywhere in your local woods, so the spores of this fungus are everywhere all the time, so having a local source of spores is unlikely to change the risk level much.

Personally I'd plant another tree now as it is bare-root fruit-tree planting season, just in case the other can't be saved. You mustn't plant a replacement in precisely the same location anyway, so you'll have to find a new location for the replacement whatever happens.