Thread terminals carry the thread's agent-browser session, so a page opened there shows in the thread's panel #73

Context

Root decision 0201 point 5 (plan DEV-6665): on a Remote Environment the Environment browser is the default browser. lazurio browser open <address> (Lazurio/LazurioPlatform#434) is what BROWSER and xdg-open run. Machines registers it (BROWSER in T3 Code's settings drop-in, among other places).

When the caller carries a T3 Code thread's session (AGENT_BROWSER_SESSION=t3-…), the command binds that session to the new tab. T3 Code already records a tab its thread's session newly binds and opens the thread's panel on it (apps/server/src/lazurio/threadTabs.ts). This works for every process T3 Code starts for a thread's provider (withAgentBrowserSession), so an agent's xdg-open or gh auth login --web shows in the thread's panel.

Gap

A thread's terminal does not get AGENT_BROWSER_SESSION. A person who runs codex login, claude auth login or gh auth login --web in a thread's terminal gets a page in the Environment browser that nobody holds. It shows only in Přehled of Nová karta, not in that thread's panel.

Proposal

Give a thread's terminal processes the same AGENT_BROWSER_SESSION the thread's provider processes get (agentBrowserSessionName(threadId)). Then a page opened from the terminal joins the thread's strip and shows in its panel, the same way an agent's does.

Acceptance

• In a thread's terminal on a Remote Environment, xdg-open https://example.com shows the page in that thread's right panel.
• No change where the Environment has no browser.