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.
