fix(site): prevent slash menu from flashing at top-left corner when closed (#27326)

Typing `/` in the agent chat input opens the skills slash menu. Pressing
Backspace to erase the `/` made the menu flash at the top-left corner of
the app for a split second before disappearing.

Radix keeps the popover content mounted through its exit animation, but
the caret-positioned `PopoverAnchor` was unmounted in the same render
that closed the menu. Without an anchor, the popper repositioned the
still-visible closing content to the viewport origin. The anchor now
stays rendered at the last known caret rect, so the menu holds its
position while it animates out.

Verified with a frame-by-frame position recorder in the browser: before
the fix the closing menu jumped from the caret position to `(0, 4)`;
after the fix it stays in place until unmount. Added a
`BackspaceClosesMenuWithoutRepositioning` story that fails without the
fix.

> This PR was created by Mux, an AI coding agent, on Mike's behalf.

site/src/pages/AgentsPage/components/ChatMessageInput/ChatMessageInput.stories.tsx

@@ -335,6 +335,33 @@ export const OutsideClickDismissesTriggerOnRefocus: Story = {
 	},
 };
 
+export const BackspaceClosesMenuWithoutRepositioning: Story = {
+	play: async ({ canvasElement }) => {
+		await typeInEditor(canvasElement, "/");
+		await findVisibleText("/reviewer");
+		const popperWrapper = () =>
+			document.querySelector<HTMLElement>(
+				"[data-radix-popper-content-wrapper]",
+			);
+		const openRect = popperWrapper()?.getBoundingClientRect();
+		expect(openRect?.left).toBeGreaterThan(0);
+		await userEvent.keyboard("{Backspace}");
+		// The closing menu must hold its position through the exit
+		// animation instead of flashing at the viewport origin.
+		let wrapper = popperWrapper();
+		for (let frame = 0; wrapper && frame < 300; frame++) {
+			const rect = wrapper.getBoundingClientRect();
+			expect({ top: rect.top, left: rect.left }).toEqual({
+				top: openRect?.top,
+				left: openRect?.left,
+			});
+			await new Promise((resolve) => requestAnimationFrame(resolve));
+			wrapper = popperWrapper();
+		}
+		expect(wrapper).toBeNull();
+	},
+};
+
 // Stories below verify that on mobile viewports, the skills popup
 // sits directly above the chat input rather than being clipped
 // above the visible viewport.

site/src/pages/AgentsPage/components/ChatMessageInput/SkillsTriggerMenu.tsx

@@ -1,3 +1,4 @@
+import { useState } from "react";
 import {
 	Command,
 	CommandEmpty,
@@ -143,6 +144,14 @@ export const SkillsTriggerMenu = ({
 			: undefined,
 	].filter((item) => item !== undefined);
 	const shouldRender = open && anchorRect;
+	// Radix keeps closing content mounted through its exit animation.
+	// Unmounting the anchor then would reposition the closing menu to
+	// the viewport origin, so keep it at the last known caret rect.
+	const [lastAnchorRect, setLastAnchorRect] = useState(anchorRect);
+	if (anchorRect && anchorRect !== lastAnchorRect) {
+		setLastAnchorRect(anchorRect);
+	}
+	const renderedAnchorRect = anchorRect ?? lastAnchorRect;
 	const shouldShowEmpty = allSkills.length === 0 && statusItems.length === 0;
 	const selectedValue = selectedIndex >= 0 ? String(selectedIndex) : "";
 
@@ -176,16 +185,16 @@ export const SkillsTriggerMenu = ({
 				}
 			}}
 		>
-			{shouldRender && (
+			{renderedAnchorRect && (
 				<PopoverAnchor asChild>
 					<span
 						aria-hidden="true"
 						style={{
 							position: "fixed",
-							top: anchorRect.top,
-							left: anchorRect.left,
+							top: renderedAnchorRect.top,
+							left: renderedAnchorRect.left,
 							width: 1,
-							height: Math.max(anchorRect.height, MIN_ANCHOR_HEIGHT_PX),
+							height: Math.max(renderedAnchorRect.height, MIN_ANCHOR_HEIGHT_PX),
 							pointerEvents: "none",
 						}}
 					/>