Desktop sidebar doesn't distinguish local / Remote Control / cloud sessions

The mobile app's session list marks each session with a laptop icon + green
"Connected" for Remote Control sessions and a cloud icon for cloud sessions.
The desktop app's Code sidebar renders every session with the same bullet, so
there is no way to tell which sessions run on another machine.

The information is clearly available to the desktop client — ListAgents from
inside a desktop session returns the kind label for each peer (Remote Control /
cloud / interactive). It just isn't surfaced in the sidebar UI.

The sidebar groups by repo instead, showing e.g. "myproject · alice". That
suffix is the repo owner, not the machine, so it can mislead: under it sits a
Remote Control session, while "myproject · bob" holds a cloud session — same
visual shape, different kind.

Neither client shows which *machine* a Remote Control session runs on. Both label
it with the repo ("alice/myproject", "bob/webapp"), which identifies the
checkout, not the host. With one remote machine you can keep it in your head; with
two or more, four rows reading "Connected" are indistinguishable. The host is known
at session creation — the CLI already defaults the RC session name prefix to the
hostname (--remote-control-session-name-prefix) — but that only helps for
auto-named sessions. A session started or renamed with a topic-based title
("HANDOFF.md review") loses the hostname entirely, and the UI has nowhere else to
carry it. Request: surface the host as its own field alongside the repo, rather
than leaving it dependent on whatever the session happens to be named.

Request: show the same kind indicator the mobile app uses, or expose it on hover.

Start at the desktop Code sidebar and trace the ListAgents data returned inside a desktop session, then compare the session indicators used by the mobile app. Done means the sidebar distinguishes local, Remote Control, and cloud sessions and exposes the Remote Control host separately from the repository, including sessions with topic-based names.

Escrito por el modelo de indexación a partir del texto del issue.