Merge.merge_commits/4 returns a merged tree but does not advance a ref or write a merge commit. Hosting products need four merge modes driven server-side:

• Merge commit: create a new commit with two parents, advance the target ref.
• Squash: collapse the source branch into one commit on the target.
• Rebase: replay the source commits on top of the target, advance.
• Fast-forward-only: refuse if not FF, otherwise just move the ref.

Scope

• Merge.merge/5(repo, target_ref, source_sha, mode, author_committer_opts) — returns {:ok, new_ref_sha} or conflict detail.
• Uses existing Authorization/hook surface via ReceivePack-style pre/post hooks so the hosting layer can veto.
• Conflict reporting: return {:error, {:conflicts, [%{path, base, ours, theirs}]}} so callers can render a UI.

Acceptance

• Each of the four modes produces a commit identical to what git merge --no-ff / --squash / git rebase / git merge --ff-only produces client-side (tree equality, not SHA equality because author/committer timestamps differ).
• Round-trip with real git: after server-side merge, git fetch from a client shows the new ref with the expected shape.