Use new set_bone_override() method (Credit: rudzik8)

.luacheckrc

@@ -0,0 +1,45 @@
+read_globals = {
+    "DIR_DELIM", "INIT",
+
+    "minetest", "core",
+    "dump", "dump2",
+
+    "Raycast",
+    "Settings",
+    "PseudoRandom",
+    "PerlinNoise",
+    "VoxelManip",
+    "SecureRandom",
+    "VoxelArea",
+    "PerlinNoiseMap",
+    "PcgRandom",
+    "ItemStack",
+    "AreaStore",
+
+    "vector",
+
+    table = {
+        fields = {
+            "copy",
+            "indexof",
+            "insert_all",
+            "key_value_swap",
+            "shuffle",
+        }
+    },
+
+    string = {
+        fields = {
+            "split",
+            "trim",
+        }
+    },
+
+    math = {
+        fields = {
+            "hypot",
+            "sign",
+            "factorial"
+        }
+    },
+}

init.lua

@@ -1,17 +1,19 @@
 local get_connected_players = minetest.get_connected_players
-local abs = math.abs
-local deg = math.deg
-local basepos = vector.new(0, 6.35, 0)
 local lastdir = {}
 
-minetest.register_globalstep(function(dtime)
+minetest.register_globalstep(function()
 	for _, player in pairs(get_connected_players()) do
 		local pname = player:get_player_name()
-		local ldeg = -deg(player:get_look_vertical())
+		local ldeg = -player:get_look_vertical()
 
-		if abs((lastdir[pname] or 0) - ldeg) > 4 then
+		if (lastdir[pname] or 0) ~= ldeg then
 			lastdir[pname] = ldeg
-			player:set_bone_position("Head", basepos, {x = ldeg, y = 0, z = 0})
+			player:set_bone_override("Head", {
+				rotation = {
+					vec = {x = ldeg, y = 0, z = 0},
+					interpolation = 0.14,
+				}
+			})
 		end
 	end
 end)

mod.conf

@@ -1,3 +1,3 @@
 name = headanim
 depends = player_api
-min_minetest_version = 5.3
+min_minetest_version = 5.9