I frequently play with the music off and I have definitely noticed this. It seems to be all trees - it was happening in the forest biome with no birchnut trees in sight, as well as the deciduous and grasslands. In the latter two, it did seem to be coming from the birchnut trees. Pretty sure I didn't hear it before the latest patch. Edit: I hear this regardless of what I'm doing, For me, it has nothing to do with chopping or interacting with the trees in any way. I hear it just walking down the path.
PS4 Pro, Don't Starve: Console Edition - Shipwrecked enabled, ROG file. I've been playing this save file for a couple of days now, and I've gotten to a point where the game seems to consistently crash in the morning on day 41 as soon as it starts to rain. Not sure why, and doing different things in between the save spawn and the crash doesn't seem to have any affect on the crash itself. Reading through the error log, it seems like maybe it has something to do with the Goose/Goose? I had the honk from the Goose/Goose spawn at the beginning of spring, but I noped outta the area and haven't seen her on my world yet. I really don't have a ton of information to add, but I've included a screenshot of the error message.