Studio: Disable text input if the limit is reached UI and update to new headers

[kozer]

Fixes https://github.com/Automattic/dotcom-forge/issues/7420

Proposed Changes

This PR updates the app to use the new quota headers.
It is also use those quotas to disable user input

Testing Instructions

• Apply the following diff:

index 282b02a..9a119e1 100644
--- a/src/hooks/use-prompt-usage.tsx
+++ b/src/hooks/use-prompt-usage.tsx
@@ -46,7 +46,7 @@ export function PromptUsageProvider( { children }: PromptUsageProps ) {
                                return;
                        }
                        setPromptLimit( limit );
-                       setPromptCount( limit - remaining );
+                       setPromptCount( limit );
                        if ( ! initiated ) {
                                setInitiated( true );
                        }

2. Navigate to Assistant tab.
3. Ensure that input is disabled.

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?

[jeroenpf]

Nice work! I see the quota updated in the UI when i interact with the AI. Also, when I apply the diff, i can no longer use the AI assistant.

We should have some feedback in the assistant tab to let the user know they can't send more messages because they reached the quota. What do you think?

[matt-west]

@jeroenpf @kozer We have some designs for that here.

[kozer]

@matt-west , @jeroenpf I'll create a new ticket for the designs, as now that the old HEAD request is missing it "breaks" Studio app.

[kozer]

Created https://github.com/Automattic/dotcom-forge/issues/7761