[FEATURE] Let the user open the Browser pane directly — toggle is inert until Claude creates a browser session

What's missing

In the Desktop app, the top-right Browser pane toggle is inert until a browser session already exists. There is no way for me, the user, to open the Browser pane and navigate somewhere myself. The only way to get a browser is to ask Claude to open a URL, which spends a model turn on something that should be a button click.

Why this is the wrong shape

The common case is: I want to look at a page, and then ask Claude about it. Today that ordering is impossible. I have to describe the page to Claude before I have the page, so Claude can open it, so I can look at it. The tool that would let me show Claude something requires me to already know what I'm showing.

This is worse than wasted clicks — it's wasted tokens. Asking "open example.com" is a full request/response cycle whose entire product is a browser window. On a metered plan that's a real cost for zero model work.

It also compounds with the login gap (#87764). For any page behind a login, the sequence is: spend a turn asking Claude to open the URL, land on a login wall, then log in by hand inside the pane anyway. The model turn bought nothing. If I could open the pane myself, the login case would at least cost zero tokens instead of one turn per site.

What I'd like

Any of these:

• Make the Browser pane toggle always live — clicking it opens the pane with a blank tab and a URL bar
• A "New browser tab" action (menu item or keyboard shortcut) that opens the pane directly
• Let the pane be opened empty and stay open across a session, so it behaves like a normal browser panel rather than an output surface Claude happens to produce

The pane already has a URL bar and is fully interactive once it exists. This is asking for one entry point into a surface that is otherwise already built.

Related but distinct

• #88965 asks for the inverse — letting Claude open the pane and read its visibility state. This request is about the user opening it.
• #87764 (no existing login state in the pane) makes this more acute but is a separate gap.
• #84322 (open a link in a new tab) assumes the pane is already open.