Automate safe merged-branch cleanup

[ByBrawe]

Add branch hygiene that removes stale same-repository branches without rebasing or re-merging old squash-merged work.

Safety rules:

• never delete the default branch or a protected branch;
• never delete a branch that backs an open PR;
• only consider same-repository merged PRs;
• require the merged PR's recorded head SHA to exactly equal the branch's current SHA;
• re-read the git ref immediately before deletion and skip it if the SHA changed;
• retain closed-unmerged diagnostics/experiments for manual review.

PRs run the planner read-only with BRANCH_HYGIENE_DRY_RUN=1; cleanup is skipped. Pushes to main and manual runs use a separate write-enabled cleanup job. The current dry-run scanned 227 branches and found 105 exact merged-head candidates while retaining 120 unmatched branches and the open-PR branch.

Merging this PR performs the first historical sweep and future main updates keep merged branch debt from accumulating.

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