diff --git a/src/vs/workbench/services/hover/browser/hover.ts b/src/vs/workbench/services/hover/browser/hover.ts
index eadb80f2df715..d5b60af62625a 100644
--- a/src/vs/workbench/services/hover/browser/hover.ts
+++ b/src/vs/workbench/services/hover/browser/hover.ts
@@ -126,6 +126,11 @@ export interface IHoverOptions {
 	 * - If there are elements in the hover to focus, focus stays inside of the hover when tabbing
 	 */
 	trapFocus?: boolean;
+
+	/**
+	 * The container to render the hover in.
+	 */
+	container?: HTMLElement;
 }
 
 export interface IHoverAction {
diff --git a/src/vs/workbench/services/hover/browser/hoverService.ts b/src/vs/workbench/services/hover/browser/hoverService.ts
index f945c707f126e..c6fbd3a8d87c8 100644
--- a/src/vs/workbench/services/hover/browser/hoverService.ts
+++ b/src/vs/workbench/services/hover/browser/hoverService.ts
@@ -59,7 +59,10 @@ export class HoverService implements IHoverService {
 			hoverDisposables.dispose();
 		});
 		const provider = this._contextViewService as IContextViewProvider;
-		provider.showContextView(new HoverContextViewDelegate(hover, focus));
+		provider.showContextView(
+			new HoverContextViewDelegate(hover, focus),
+			options.container
+		);
 		hover.onRequestLayout(() => provider.layout());
 		if ('targetElements' in options.target) {
 			for (const element of options.target.targetElements) {
@@ -70,16 +73,10 @@ export class HoverService implements IHoverService {
 		}
 		const focusedElement = <HTMLElement | null>document.activeElement;
 		if (focusedElement) {
-			hoverDisposables.add(addDisposableListener(focusedElement, EventType.KEY_DOWN, e => this._keyDown(e, hover)));
-			hoverDisposables.add(addDisposableListener(document, EventType.KEY_DOWN, e => this._keyDown(e, hover)));
+			hoverDisposables.add(addDisposableListener(focusedElement, EventType.KEY_DOWN, e => this._keyDown(e, hover, !!options.hideOnKeyDown)));
+			hoverDisposables.add(addDisposableListener(document, EventType.KEY_DOWN, e => this._keyDown(e, hover, !!options.hideOnKeyDown)));
 			hoverDisposables.add(addDisposableListener(focusedElement, EventType.KEY_UP, e => this._keyUp(e, hover)));
 			hoverDisposables.add(addDisposableListener(document, EventType.KEY_UP, e => this._keyUp(e, hover)));
-			if (options.hideOnKeyDown) {
-				hoverDisposables.add(addDisposableListener(focusedElement, EventType.KEY_DOWN, () => {
-					this.hideHover();
-					this._lastFocusedElementBeforeOpen?.focus();
-				}));
-			}
 		}
 
 		if ('IntersectionObserver' in window) {
@@ -110,7 +107,7 @@ export class HoverService implements IHoverService {
 		}
 	}
 
-	private _keyDown(e: KeyboardEvent, hover: HoverWidget) {
+	private _keyDown(e: KeyboardEvent, hover: HoverWidget, hideOnKeyDown: boolean) {
 		if (e.key === 'Alt') {
 			hover.isLocked = true;
 			return;
@@ -120,7 +117,7 @@ export class HoverService implements IHoverService {
 		if (keybinding.getSingleModifierDispatchChords().some(value => !!value) || this._keybindingService.softDispatch(event, event.target)) {
 			return;
 		}
-		if (!this._currentHoverOptions?.trapFocus || e.key !== 'Tab') {
+		if (hideOnKeyDown && (!this._currentHoverOptions?.trapFocus || e.key !== 'Tab')) {
 			this.hideHover();
 			this._lastFocusedElementBeforeOpen?.focus();
 		}
@@ -129,7 +126,7 @@ export class HoverService implements IHoverService {
 	private _keyUp(e: KeyboardEvent, hover: HoverWidget) {
 		if (e.key === 'Alt') {
 			hover.isLocked = false;
-			// Hide if alt is released while the mouse os not over hover/target
+			// Hide if alt is released while the mouse is not over hover/target
 			if (!hover.isMouseIn) {
 				this.hideHover();
 				this._lastFocusedElementBeforeOpen?.focus();