Re-read this tenant's GitHub installations from GitHub and re-sync them.

The recovery path for the failure this module's discovery backoff narrows but cannot close: an install whose repository set was still empty on every read inside the callback's budget. Nothing else ever re-reads it -- the installation webhook covers suspend/resume, installation_repositories only a later add/remove -- so without this the stored empty set is permanent and the wizard's "Retry" just re-reads our own database and fails identically forever. This makes that button do the one thing that can actually help.

Reports what is true rather than inferring it from the repository count, so the caller can tell "GitHub is not connected" apart from "GitHub is connected and shared no repositories" -- two states the wizard used to collapse into a single, terminal-sounding "no verified installation was found".

SETTINGS_MANAGE, the same permission that issued the install URL: this re-reads third-party state for the tenant and rewrites repository rows.