It's been two month since the branches were cut, and the water has been dripping from it since then; a small pond has formed. Is this something to be worried about?
I don't think it's as serious an issue as others do. For one thing, my father just completed this year's sap collection season for making Maple syrup. If you saw how much sap comes out of a single small tree you'd be less concerned.
For another, it seems like the wound is sealing over as nature intended. I have oak trees which naturally leak all summer in a similar manner. It's how trees do.
For yet another, two months ago was basically winter in much of the world. That's not a bad time to do pruning.
Unless you encounter an extraordinarily severe drought this year, I'd expect a tree of that size to recover without issue.
Whoever cut that when they cut it was not a very good excuse for a tree surgeon.
That's not water, it's sap. Eventually it will stop, but doing major surgery on hardwoods in the early spring is exceedingly stupid, because this happens, and the tree is severely weakened by what is, essentially "blood loss" - and it would not happen (either "at all" or to nearly that extent) if the same cut was made in the summer.
The cut facing us may also be cut too close to the trunk. The one we see the side of looks OK, but this one looks like it might have been cut beyond the "branch collar" which is the formation at the base of the branch that will, if not cut off, more quickly heal over a cut branch
Wow, That's sap, not water. It's very unhealthy for the tree to be loosing that much. Check with your agricultural department or department of forestry to see if they can recommend a sealer or cap for that. Growing up in the midwest, our tree trimmers always coated the cut with a tar like substance but as @Ecnerwal pointed out, that's no longer being done.