The documenter writes and commits docs onto the task branch in its own
workspace clone, but i_documented had no push step — so the commit stayed
local and the PM merged the already-open PR without the docs, which then
vanished on merge. i_documented now pushes the task branch before handoff,
mirroring the developer's _ensure_branch_pushed; a push failure holds the
task in awaiting_documentation for a retry instead of silently dropping the
docs. Extract _finalize_documented to keep the verb under the return-count
ceiling.