In my experience, broken tree branches come from:

• Crazy angles on the supports. This happens when a support needs to 'grow' over the print in order reach the thing it needs to support. This ultimately comes down to part geometry, so there's not a ton you can do here if you can't change the geometry or orientation of the part
• Poor bed adhesion causing the trunk to separate from the bed. Clean your bed with dish soap and dry it with paper towels. Make sure you have a good first layer by getting your your bed and gantry in parallel planes and double check your z-offset. Bonus points if you can do a bed mesh between prints
• The extruder catching on a branch and breaking it off. This is usually due warping or over-extrusion. Warping can be its own rabbit hole. Over-extrusion is easy to tune for, especially if your slicer has built in calibration aids (eg OrcaSlicer, SuperSlicer, etc)
• An ambitious slicer not making the supports themselves very strong. Slicers these days seem to avoid thin/tall trees, but they're still usually single perimeter. I've configured my slicer to use 0.6mm thick walls on supports
• If you have a bed slinger, tall supports can wobble. Slowing down acceleration/jerk is really the only way to combat this

Obviously, these can all be a bit interrelated.

The support in this print is basically vertical (no crazy angles), I generally have great bed adhesion/my printer can mechanically make its gantry in plane with the bed/I run a bed mesh every print/I use klipper_z_calibration to get a consistent first layer, nothing's warping and I've tuned my extrusion multiplier for this spool of filament, the support itself is strong due to its girth at the base and wall thickness, and CoreXY means that the support doesn't really move unless the extruder is dragging some.