Updated CPM to the newest fabric version [v0.6.18a] for 1.21, added some animations to my model and attempted to export it as a .cpmmodel file. In doing so, trying to change the export option to model from skin, it dropped an error:
logs.json

{ "entries": [ { "msg": { "args": [ "Error processing mouse event" ], "key": "label.cpm.identity" }, "level": "ERROR", "time": "191af35d035", "error": "java.lang.NullPointerException: Cannot invoke \"com.tom.cpm.shared.parts.ModelPartLink.getLink()\" because \"link\" is null\n\tat com.tom.cpm.shared.editor.gui.popup.ExportPopup$Model.updateLink(ExportPopup.java:667)\n\tat com.tom.cpm.shared.editor.gui.popup.ExportPopup$Model.\u003cinit\u003e(ExportPopup.java:610)\n\tat com.tom.cpm.shared.editor.gui.popup.ExportPopup.lambda$new$0(ExportPopup.java:60)\n\tat com.tom.cpl.gui.elements.Button.mouseClick(Button.java:39)\n\tat com.tom.cpl.gui.elements.GuiElement.mouseClick(GuiElement.java:47)\n\tat com.tom.cpl.gui.elements.Panel.mouseClick(Panel.java:46)\n\tat com.tom.cpl.gui.elements.Panel.mouseClick(Panel.java:46)\n\tat com.tom.cpl.gui.Frame$PopupLayer.mouseClick(Frame.java:244)\n\tat com.tom.cpl.gui.elements.Panel.mouseClick(Panel.java:46)\n\tat com.tom.cpl.gui.elements.Panel.mouseClick(Panel.java:46)\n\tat com.tom.cpm.client.GuiImpl.method_25402(GuiImpl.java:250)\n\tat net.minecraft.class_312.method_1611(class_312.java:107)\n\tat net.minecraft.class_437.method_25412(class_437.java:431)\n\tat net.minecraft.class_312.method_1601(class_312.java:107)\n\tat net.minecraft.class_312.method_22686(class_312.java:196)\n\tat net.minecraft.class_1255.execute(class_1255.java:108)\n\tat net.minecraft.class_312.method_22684(class_312.java:196)\n\tat org.lwjgl.glfw.GLFWMouseButtonCallbackI.callback(GLFWMouseButtonCallbackI.java:43)\n\tat org.lwjgl.system.JNI.invokeV(Native Method)\n\tat org.lwjgl.glfw.GLFW.glfwPollEvents(GLFW.java:3438)\n\tat com.mojang.blaze3d.systems.RenderSystem.pollEvents(RenderSystem.java:150)\n\tat com.mojang.blaze3d.systems.RenderSystem.flipFrame(RenderSystem.java:168)\n\tat net.minecraft.class_1041.method_15998(class_1041.java:303)\n\tat net.minecraft.class_310.method_1523(class_310.java:1307)\n\tat net.minecraft.class_310.method_1514(class_310.java:882)\n\tat net.minecraft.client.main.Main.main(Main.java:256)\n\tat net.fabricmc.loader.impl.game.minecraft.MinecraftGameProvider.launch(MinecraftGameProvider.java:480)\n\tat net.fabricmc.loader.impl.launch.knot.Knot.launch(Knot.java:74)\n\tat net.fabricmc.loader.impl.launch.knot.KnotClient.main(KnotClient.java:23)\n\tat org.prismlauncher.launcher.impl.StandardLauncher.launch(StandardLauncher.java:100)\n\tat org.prismlauncher.EntryPoint.listen(EntryPoint.java:129)\n\tat org.prismlauncher.EntryPoint.main(EntryPoint.java:70)\n" }, ], "name": "MoonlitComet", "platform": "Minecraft 1.21 (fabric/0.16.3/0.102.0+1.21) 0.6.18a" }

Downgrading to the previous 1.21 version for Fabric seemed to fix it for now, so it appears to be a bug with the latest version.