Enhance/Add "Search entire recent tasks" feature to IDE Extension

What variant of Codex are you using?

IDE Extension

What feature would you like to see?

Please enhance the "search recent tasks" capability in the IDE Extension to allow for searching through entire tasks. Ref #13035 and #13038

Additional information

In the Cloud UI the title can be determined by the assistant using the initial task prompt. It's possible and likely that a generated title will not include relevant keywords which are used in the initial prompt of a task.

The user/developer might be looking for a task that processed a specific file or UI platform, or which included a specific error message or GH Issue#. This context is in the task history, not the description. The current task mechanism won't find it.

Note from #13035 that to be complete, a search must be able to find text within links, code, and both prompts and responses.

Now that we've all been using these tools for a long time, there's a lot of history in the long list of tasks. The simple search implemented for v0 is helpful but no longer adequate.

That leads to other possible enhancements in this area. Examples:

• The ambiguity of which tasks are "recent" might need to be defined, or user-configurable (separate feature?), to limit the scope of detailed searches and avoid long delays.
• Consider a dropdown to only search within prompts, responses, filenames, or links.
• Consider other controls for some form of time range (day limit, date start/end).

If these are considered to be worthy enhancements, in-line with the product direction, I'll add them.

Thanks.