It seems like something may be killing this tree. The sap oozing seems to have happened over night. The oozing is different colors with the clear sap sites higher than the others. And the sap is oozing on all sides of the tree at approximately the same height. What is causing this? Will it kill the tree?
This looks like a cherry tree. These trees can exude sap/gum due to any type of stress such as pruning cuts, wounds, cankers, or possible insect pests such as the peach tree borer. If you see some 'sawdust'-like material (frass) on the ground below the holes or in the sap exuding from the holes, it could be an indicator of borers. There are no chemical controls for the above.
In general cherry trees are not long lived trees. At this point all you can do is prune dead wood and prune damaged areas back to healthy tissue. If this is in the main trunk this is not possible. The best recommendation is to keep the tree watered during dry periods. Make sure mulch is no thicker than several inches and away from the trunk. If the canopy looks good all you can do is enjoy the tree and it sounds like you may have to consider removal in the future.
Here is more on ornamental fruit trees https://extension.umd.edu/sites/extension.umd.edu/files/_docs/programs/hgic/HGIC_Pubs/TreesandShrubs...