feat(tabs): every agent tab shows its CLI logo, claude included

A claude tab drew no harness mark at all and every other agent CLI a
two-letter text pill (DS, CX, ...), so a claude tab read as "no harness"
next to its neighbours. Session tabs (header strip, side rail, sidebar,
phone chips) and the desktop home rail now draw the agent through PR
#532's run-mode-dot <id> slot, the id as data, the same mark the Run
menus and the tile and split headers use. The shell is not an agent and
keeps its SH pill; a CLI added through clis.json gets the slot's plain
dot instead of nothing.

The per-CLI tab pill colours and their light-skin ink overrides are gone
(the monochrome marks follow the tab's own text colour), and the logo
steps aside with the other adornments while a compact rail row renames.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

docs/cli-registry.md

@@ -36,7 +36,7 @@ These are the only writes to `clis.json`. They are serialized, and a file that d
 interface CliEntry {
   id: CliId; // 'codex'
   label: string; // 'Codex' — shown in menus
-  shortBadge: string; // tab badge, e.g. 'CX'
+  shortBadge: string; // short label ("Run CX", the Settings CLI list), e.g. 'CX'; tabs show the run-mode-dot logo instead
   accent: string; // single hex colour
   enabled: boolean;
   stock: boolean; // set by the loader; a custom entry can never claim it