Skip the desktop update restart prompt when nothing is running

[1337Crakker]

Problem

Installing a downloaded desktop update always asks "Install update X and restart T3 Code? Any running tasks will be interrupted." This happens even when nothing is running. Most installs happen while idle, so the prompt becomes something people click through, which makes it worth less on the occasions when work really is running.

Proposal

Skip the prompt only when the app can show that nothing it's about to stop is working. Otherwise keep the prompt exactly as it is today.

A desktop install stops every backend the app runs: the local server and any WSL servers the app runs. Each one has to be known idle:

• its thread list is live, not a cached copy or in the middle of a resync;
• no thread has a live run, a pending approval or question, or pending background tasks. This is the same isLiveSubagentShell rule the shell stream uses so that it never drops live threads;
• its terminal list has loaded and no terminal is running a command (hasRunningSubprocess).

Anything unknown keeps the prompt: the catalog isn't ready, an environment is disconnected or disabled, terminals haven't loaded, or the desktop reports a running backend the client can't see.

Work started from a phone or app.t3.codes on this machine runs on its server, so it counts. SSH-launched servers run under nohup and survive the restart, so they don't count.

Prior art

The Codex desktop app does this more loosely. It warns only if a window reports an in-progress local conversation, it ignores terminals and background work, and on macOS it skips the warning when the state is unknown.

Out of scope and known limits

• The Update everything dialog (the multi-machine summary) is unchanged, as are remote server updates and mobile.
• Threads archived while waiting on an approval or with background tasks running aren't in the shell. The server side of that is in fix(server): reject archiving threads with active turns #23451.
• Work that starts between the click and the shutdown can still be interrupted. Terminal commands are detected by the server's subprocess poll, about once a second. Today's prompt has the same gap after Confirm.

Implementation: #28187 (small, web-only, with before/after screenshots).

Is this direction and scope OK with a maintainer?