Move subagents into session side panel

PLAN.md

@@ -976,6 +976,16 @@ SSE stream, reused by addressing rather than by copying — costs a routing step
 in the translator and a registry (`session/subagent.rs`) rather than a second
 session type with a driver, a process and a config entry it does not need.
 
+**The phone presents them beside their open session, not inside the main
+session list** (changed 2026-09-17). A left swipe pulls a panel over the live
+transcript; the transcript remains composed beneath it so opening the panel or
+a child's read-only transcript does not stop its stream, discard its draft or
+lose its scroll position. Horizontal transcript content keeps first claim on
+the gesture; collapsing it or starting on the ordinary session surface gives
+the gesture back to the panel, while Android keeps its own edge Back gesture.
+This is also the intended home for background work once that has a list of its
+own; only subagents are shown there now.
+
 ### HTTP surface
 
 **`routes.rs`'s module doc comment is the table.** REST for actions, one SSE