[Backport 5.5.x] Upgrade cody web experimental package to 0.2.7 (#63863) (#63901)

backport https://github.com/sourcegraph/sourcegraph/pull/63863

S2 Cody Web is broken at the moment. New client-config handlers fail
with 401 status because we don't send custom headers, this works for gql
queries since they all are POST requests and the browser automatically
sends an Origin header for them and this is enough for our auth
middleware to check cookies, but with client-config which is rest it's
not the case and we should send `X-Requested-Client: Sourcegraph` header
to make our auth middleware to pass this query correctly

Note that this problem doesn't exist in local builds since we proxy all
requests and add `X-Requested-Client: Sourcegraph` in dev server.

See Cody latest build PR for more details
https://github.com/sourcegraph/cody/pull/4898

## Test plan

CI

Co-authored-by: Vova Kulikov <vovakulikov@icloud.com>

Author: michaellzc

client/web/src/cody/chat/new-chat/NewCodyChatPage.tsx

@@ -31,7 +31,11 @@ export const NewCodyChatPage: FC<NewCodyChatPageProps> = props => {
             <CodyPageHeader isSourcegraphDotCom={isSourcegraphDotCom} className={styles.pageHeader} />
 
             <div className={styles.chatContainer}>
-                <CodyWebChatProvider accessToken="" serverEndpoint={window.location.origin}>
+                <CodyWebChatProvider
+                    accessToken=""
+                    serverEndpoint={window.location.origin}
+                    customHeaders={window.context.xhrHeaders}
+                >
                     <CodyWebHistory>
                         {history => (
                             <div className={styles.chatHistory}>

client/web/src/cody/sidebar/new-cody-sidebar/NewCodySidebarWebChat.tsx

@@ -48,6 +48,7 @@ export const NewCodySidebarWebChat: FC<NewCodySidebarWebChatProps> = memo(functi
             chatID={chatID}
             initialContext={contextInfo}
             serverEndpoint={window.location.origin}
+            customHeaders={window.context.xhrHeaders}
             onNewChatCreated={handleNewChatCreated}
         >
             <ChatUi />

package.json

@@ -333,7 +333,7 @@
     "bloomfilter": "^0.0.18",
     "buffer": "^6.0.3",
     "classnames": "^2.2.6",
-    "cody-web-experimental": "^0.2.5",
+    "cody-web-experimental": "^0.2.7",
     "comlink": "^4.3.0",
     "copy-to-clipboard": "^3.3.1",
     "core-js": "^3.8.2",