diff --git a/src/vs/workbench/contrib/remote/browser/remoteIndicator.ts b/src/vs/workbench/contrib/remote/browser/remoteIndicator.ts
index 7570ab29201..711097dba4a 100644
--- a/src/vs/workbench/contrib/remote/browser/remoteIndicator.ts
+++ b/src/vs/workbench/contrib/remote/browser/remoteIndicator.ts
@@ -273,15 +273,15 @@ export class RemoteStatusIndicator extends Disposable implements IWorkbenchContr
 
 	private updateRemoteStatusIndicator(): void {
 
-		// Remote Indicator: show if provided via options
+		// Remote Indicator: show if provided via options, e.g. by the web embedder API
 		const remoteIndicator = this.environmentService.options?.windowIndicator;
 		if (remoteIndicator) {
 			this.renderRemoteStatusIndicator(truncate(remoteIndicator.label, RemoteStatusIndicator.REMOTE_STATUS_LABEL_MAX_LENGTH), remoteIndicator.tooltip, remoteIndicator.command);
 			return;
 		}
 
-		// Remote Authority: show connection state
-		if (this.remoteAuthority) {
+		// Show for remote windows on the desktop, but not when in code server web
+		if (this.remoteAuthority && !isWeb) {
 			const hostLabel = this.labelService.getHostLabel(Schemas.vscodeRemote, this.remoteAuthority) || this.remoteAuthority;
 			switch (this.connectionState) {
 				case 'initializing':
@@ -305,7 +305,9 @@ export class RemoteStatusIndicator extends Disposable implements IWorkbenchContr
 				}
 			}
 			return;
-		} else if (this.virtualWorkspaceLocation) {
+		}
+		// show when in a virtual workspace
+		if (this.virtualWorkspaceLocation) {
 			// Workspace with label: indicate editing source
 			const workspaceLabel = this.labelService.getHostLabel(this.virtualWorkspaceLocation.scheme, this.virtualWorkspaceLocation.authority);
 			if (workspaceLabel) {
@@ -316,7 +318,7 @@ export class RemoteStatusIndicator extends Disposable implements IWorkbenchContr
 				} else {
 					tooltip.appendText(nls.localize({ key: 'workspace.tooltip', comment: ['{0} is a remote workspace name, e.g. GitHub'] }, "Editing on {0}", workspaceLabel));
 				}
-				if (!isWeb) {
+				if (!isWeb || this.remoteAuthority) {
 					tooltip.appendMarkdown('\n\n');
 					tooltip.appendMarkdown(nls.localize(
 						{ key: 'workspace.tooltip2', comment: ['[features are not available]({1}) is a link. Only translate `features are not available`. Do not change brackets and parentheses or {0}'] },
diff --git a/test/automation/src/application.ts b/test/automation/src/application.ts
index 2a771d2c378..a3adfffe383 100644
--- a/test/automation/src/application.ts
+++ b/test/automation/src/application.ts
@@ -140,8 +140,8 @@ export class Application {
 		await code.waitForWindowIds(ids => ids.length > 0);
 		await code.waitForElement('.monaco-workbench');
 
-		// Web or remote: wait for a remote connection state change
-		if (this.remote || this.web) {
+		// Remote but not web: wait for a remote connection state change
+		if (this.remote) {
 			await code.waitForTextContent('.monaco-workbench .statusbar-item[id="status.host"]', undefined, s => {
 				this.logger.log(`checkWindowReady: remote indicator text is ${s}`);