fix(web): reclaim overlay scrollbar gutter

packages/client/ui-conversation/src/client/skeleton/ConversationRoot.module.css

@@ -272,12 +272,17 @@
 .scrollBody:has([data-conversation-composer-overlay]) {
   position: relative;
   /* A clipping box nothing scrolls out of, stated as a scroll container on both
-     axes rather than `overflow: hidden`: WebKit honours the reservation above
-     only in the `overflow-y: auto` form, and a single-axis scroller computes
-     the other axis to `auto`
-     ([decision](../../../../../../.agents/notes/implemented/bug-fix/2026-08-04-composer-tab-gutter-reservation.md)). */
+     axes rather than `overflow: hidden`: a single-axis scroller computes the
+     other axis to `auto`, and the seat's absolute positioning below needs the
+     box to stay a containing block in every engine. */
   overflow-x: hidden;
   overflow-y: auto;
+  /* The view owns its own scrollers (the trajectory ledger scrolls inside the
+     view), so this box never scrolls here; reserving a gutter would only
+     narrow the view's content by the bar's width. Chat keeps the reservation
+     on the same element, so the seat below compensates with the bar's width
+     ([decision](../../../../../../.agents/notes/implemented/bug-fix/2026-08-04-composer-tab-gutter-reservation.md)). */
+  scrollbar-gutter: auto;
 }
 
 .scrollBody:has([data-conversation-composer-overlay]) > .viewArea {
@@ -288,7 +293,13 @@
 
 .scrollBody:has([data-conversation-composer-overlay]) > .composerSeat {
   position: absolute;
-  right: 0;
+  /* Chat's seat rides this box's content box, which its own scrolling shortens
+     by the bar's width; the overlay seat is against the padding box, so it
+     must give back the same width to keep the input card in place across
+     tabs. Reads ui-theme's --dsh-scrollbar-width, which mirrors the WebKit
+     bar's layout width; Firefox's thin bar resolves to the same 8px on the
+     platforms this app targets, so the compensation holds there too. */
+  right: var(--dsh-scrollbar-width);
   bottom: 0;
   left: 0;
 }

packages/client/ui-theme/src/styles/scrollbar.css

@@ -17,6 +17,11 @@
 body {
   --dsh-scrollbar-thumb: var(--dsw-alias-scrollbar-bg-l1);
   --dsh-scrollbar-thumb-hover: var(--dsw-alias-scrollbar-hover-l1);
+  /* The WebKit bar's layout width, mirrored by the ::-webkit-scrollbar rule
+     below. A surface that must align itself beside a space-consuming bar
+     (ConversationRoot's overlay composer seat) reads this instead of
+     hardcoding the number. */
+  --dsh-scrollbar-width: 8px;
 }
 
 /* The two paths are mutually exclusive, and the gate is load-bearing rather