Cutting a wide internal keyway is one of those jobs where the setup fights you the whole way, and that is exactly the problem this build is wrestling with. The workpiece is a large, thick-walled cylinder clamped down on a metal machine table, and the cut runs inside its hollow interior, where there is little room to hide from vibration.
The way it is put together is straightforward but interesting to watch. A cylindrical horizontal tool bar reciprocates linearly through the bore, and a cutting tool mounted at the end of the bar slices material on each stroke. Successive horizontal passes along the bottom of the channel form a flat-bottomed trough, and the maker is taking about 1 mm per pass. Metal chips and swarf gather on the inner far lip after each stroke, so there is clearly a lot of material moving around in there.
What stands out is where the job has got to: the maker is about 1 mm from the final depth, and vibration is showing up right at this stage. Plenty of cutting lubricant has already been applied, but the chatter persists. The close-up at the end shows the surface texture and parallel machining marks on the cut floor, which gives a good look at the finish being chased.
The plan from here is sensible in my view: check the insert and try a fresh cutting edge, reduce tool overhang, lower the RPM, take lighter cuts, and look into rubber straps to dampen the vibration. Whether the straps will settle it, or whether a fresh edge alone does the trick, is still an open question.