* feat(desktop): add background-task indicator to sidebar session rows
A session with a live terminal(background=true) process but no active LLM
turn now shows a pulsing gray dot in the sidebar — distinct from the accent
pulse of an active turn and the steady amber/green of needs-input/unread.
New $backgroundRunningSessionIds computed atom joins
$backgroundStatusBySession (runtime-keyed) with $sessionStates
(runtime→stored) to produce stored session ids the sidebar row can match
against — same pattern as $attentionSessionIds and $unreadFinishedSessionIds.
Also refactors SidebarRowDot from a 3-branch if-else chain into a
table-driven priority array of DotState entries. Each state declares its
active flag, className, ariaLabel, and title in one place — adding a new
indicator state is now one array entry instead of another conditional.
* fix(desktop): keep pulse-dot before:bg-* static so Tailwind emits it
The PING() helper interpolated the color into `before:bg-${color}`, but
Tailwind v4 only generates utilities it finds as complete static strings — a
template-composed `before:bg-(--ui-accent)` / `before:bg-muted-foreground/50`
is never emitted, so both pulse rings (working + new background) lost their
halo color. Make PING a static scaffold and write the before:bg color inline
per variant.
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Co-authored-by: Brooklyn Nicholson <brooklyn.bb.nicholson@gmail.com>
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