feat(gstack): share the Playwright bump, report the browser cache

Extract gstack_bump_playwright_if_unsupported from install-plugins.sh into
lib/gstack-playwright.sh and call it from update-all.sh too. A submodule
update no longer leaves the OS-support bump unapplied until the next
`make plugin` — that was BDR-029's open caveat.

The update helper never touches the submodule working tree: on failure it
prints git's own message and points at `make plugin`, and returns non-zero
so the existing `else warn` arm still handles it.

Add a read-only `Playwright browsers` section to doctor.sh: cache size,
which registered install requires each revision, and counts of unreferenced
directories and broken links. No pruning is written — Playwright's own
`install` already unions the required set across every registered install,
and all three installs here are live (rev 1228 for gstack + gsd-pi 1.61,
rev 1243 for gsd-pi 1.63).

Carries two latent-bug fixes from the moved code: the ostag capture exited
1 on every non-Ubuntu host and aborted the caller under inherited errexit,
and the bun calls had no timeout.

update-all.sh

@@ -15,8 +15,10 @@ REPO="$(cd "$(dirname "$0")" && pwd)"
 VERSION=$(cat "$REPO/version.txt" 2>/dev/null || echo "unknown")
 
 # Load shared detection library
-# shellcheck source=lib/detect-plugins.sh
+# shellcheck source=lib/detect-plugins.sh disable=SC1091
 source "$REPO/lib/detect-plugins.sh"
+# shellcheck source=lib/gstack-playwright.sh disable=SC1091
+source "$REPO/lib/gstack-playwright.sh"
 
 echo ""
 echo "═══ claude-config update (v${VERSION}) ═══"
@@ -84,7 +86,7 @@ if [[ "$_gstack_confirm" =~ ^[Yy]$ ]]; then
     _gstack_state=$(bash "$REPO/lib/toggle-external.sh" status gstack 2>/dev/null || echo "unknown")
   fi
 
-  if git submodule update --remote skills-external/gstack 2>/dev/null; then
+  if gstack_submodule_update_with_bump "$REPO"; then
     if [ -d "skills-external/gstack" ]; then
       if [ -x "skills-external/gstack/setup" ]; then
         if (cd skills-external/gstack && ./setup) 2>/dev/null; then