[web] Gate new reusable sharing links behind sharing-updates-new-link (#35412)

Ship the new share-project modal (behind sharing-updates) wired to the
legacy token-based link sharing, and hide the new reusable-link
functionality (anyone with the link / group links) behind a new
sharing-updates-new-link split test.

- With the flag off, the modal offers two options, "Only invited people"
  and "Via sharing links", both driven by publicAccessLevel; the reusable
  -link options, privileges dropdown and copy-sharing-link button are hidden.
- Enable the flag in the acceptance tests that exercise those routes: a
  seeded split test in saas, splitTestOverrides in non-saas.

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: thomas- <2176518+thomas-@users.noreply.github.com>
GitOrigin-RevId: 3f34a2da5dbdc6f27ed389f9c25eea66143b8160

services/web/app/src/Features/Project/ProjectController.mjs

@@ -498,6 +498,7 @@ const _ProjectController = {
       'overleaf-code',
       'export-docx',
       'sharing-updates',
+      'sharing-updates-new-link',
       'export-markdown',
       'export-html',
       'command-palette',