When I chop trees I hear the switch tools sound. In the footage provided (sorry about the low quality, turn the volume to the max to hear the sound clearly) you'll hear the tool switching sound at the start of the chop and at 96% and 90% of the axe's durability.
When switching to any tool your suppose to hear a sound, but they are not supposed to make sounds when using the tools in game. I have never heard tools make sounds like this in the Pc version or in the orginal Don't Starve game on console/ Pc.
Steps to Reproduce
Get an Axe and chop Trees.
This issue has not been confirmed by a developer yet.