Studio: Implement disable chat UI when the user reaches prompt limit

[katinthehatsite]

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

Proposed Changes

This PR adds UI for the case when the user has reached the limit of prompts. When the chat is new:

When the user has previous messages in chat:

Testing Instructions

• Pull the changes from this branch locally
• Start the app with the AI Assistant: STUDIO_AI=true npm start
• 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 );
                        }

• Navigate to the AI Assistant
• Confirm that you see the message that the chat is disabled along with the count of days in which your input will be reset
• If it is a new chat, confirm that no Welcome Component is disabled
• If it is an old chat, confirm that you can see previous messages but can't send a new message

Pre-merge Checklist

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

[katinthehatsite]

Please note that I have not disabled Clear conversation button in the UI. I am not sure if it should disabled? I see both sides: the user should be able to clear stored conversation but it might give an impression to the user that by doing that, they will reset the prompts. Any thoughts?

[matt-west]

Please note that I have not disabled Clear conversation button in the UI. I am not sure if it should disabled? I see both sides: the user should be able to clear stored conversation but it might give an impression to the user that by doing that, they will reset the prompts. Any thoughts?

I think it makes sense to keep the Clear conversation button accessible.