AI Chat fullpage should be able to attach a Tab

[petemill]

There's no way to associate a new conversation opened in FullPage with a Tab. We could show a filterable list of open tabs (in the same way as TabSearch) and just ask the current Service to attach the Conversation to whichever Tab is chosen.

Background

Currently, when you create a new Full Page conversation, there is no way to associate that conversation with an open tab (as opposed to a new conversation in the sidebar, where the chat is tied to the currently open tab).

We should introduce some new UI for picking a currently open tab to associate with the conversation. As an added bonus, this will pave the way for associating multiple tabs/contents with a single conversation.

For the UI we'll implement the same UI as for multiple tab contexts, but with a radio button instead of a checkbox. When multi tab conversations are ready, we can swap over to a checkbox:

UX Designs: https://www.figma.com/design/m0Gdbf0wtqyfEFGm32VLLc/%F0%9F%94%84-Leo-%5BIN-PROGRESS%5D?node-id=6873-71134&p=f&t=oUSOFioeEJRg8rYD-0

Approach

This feature will be split in two parts:

1. Implement the C++ side service for getting a list of currently open tabs across browser windows in the current process ([AI Chat]: Add service for getting currently open tabs in all windows for the current project #43221)
2. Implement the front end for the feature ([AI Chat]: Add UI for picking a tab to associate with the current conversation #43222)

AI Chat Projects

#43189