feat(live): board dynamique sans refresh (issue #15)

Diffusion SSE sur toutes les mutations (move, création, capture,
étiquettes) via _publish_board_changed; GET /api/board/{o}/{r}
(fragments _card.html rendus serveur, même pipeline que la page);
board-live.js: diff en place par colonne avec animation FLIP,
application différée pendant un drag, filtres/compteurs réappliqués,
repli par sondage 45 s sans webhooks. Carte extraite en partiel
_card.html partagé page/API.

app/main.py

@@ -258,6 +258,16 @@ class LiveHub:
 hub = LiveHub()
 
 
+async def _publish_board_changed(repo_full_name: str) -> None:
+    """Tell every connected client this repo's board changed (#15).
+
+    Called after each mutation Kanbante knows about (move, create,
+    capture, label toggle). Webhooks broadcast separately with a
+    richer payload; board clients accept both shapes.
+    """
+    await hub.broadcast({"repo": repo_full_name, "type": "board-changed"})
+
+
 # ── Templates ──────────────────────────────────────────────
 
 _tpl_env = Environment(
@@ -554,6 +564,67 @@ async def board(request: Request, owner: str, repo: str, milestone: str = ""):
     )
 
 
+def _board_columns_for(
+    owner: str, repo: str, all_items: list[dict], milestone: str = ""
+) -> tuple[dict[str, list[dict]], list[dict], dict]:
+    """Reconcile + merge pipeline shared by the board page and its
+    JSON twin (issue #15). Returns (columns, display_issues, state)."""
+    full_name = f"{owner}/{repo}"
+    issues = [i for i in all_items if _is_issue(i)]
+    open_issues = [i for i in issues if i.get("state") == "open"]
+    closed_numbers = {i["number"] for i in issues if i.get("state") != "open"}
+    open_numbers = {i["number"] for i in open_issues}
+    changes = reconcile_board_state(full_name, open_numbers, closed_numbers)
+    for number in changes["closed_numbers"]:
+        log_event(full_name, number, "closed", to_column="done", source="gitea")
+    _adopt_label_columns(full_name, open_issues, get_board_state(full_name))
+    display_issues = open_issues
+    if milestone:
+        def _in_ms(issue: dict) -> bool:
+            ms = issue.get("milestone") or {}
+            return bool(ms) and (
+                str(ms.get("id")) == milestone or ms.get("title") == milestone
+            )
+
+        display_issues = [i for i in open_issues if _in_ms(i)]
+    board_state = get_board_state(full_name)
+    columns = _merge_issues_with_board(display_issues, board_state)
+    return columns, display_issues, board_state
+
+
+@app.get("/api/board/{owner}/{repo}")
+async def api_board(owner: str, repo: str, milestone: str = ""):
+    """The board as JSON + server-rendered card fragments (issue #15).
+
+    The board page swaps these fragments in place when the board
+    changes elsewhere — same merge/reconcile pipeline as the HTML
+    page, so label adoptions and closures are reflected identically.
+    """
+    full_name = f"{owner}/{repo}"
+    all_items = await gitea.get_repo_issues(owner, repo, state="all")
+    columns, display_issues, board_state = _board_columns_for(
+        owner, repo, all_items, milestone
+    )
+    settings = get_settings()
+    ages = _card_ages(full_name, display_issues, board_state)
+    card_template = _tpl_env.get_template("_card.html")
+    payload: dict[str, dict] = {}
+    for col in KANBAN_COLUMNS:
+        cards = columns[col]
+        if cards:
+            html = "".join(
+                card_template.render(
+                    issue=issue, ages=ages,
+                    aging_days=settings.aging_days, full_name=full_name,
+                )
+                for issue in cards
+            )
+        else:
+            html = '<p class="column-empty">Glissez une carte ici</p>'
+        payload[col] = {"count": len(cards), "html": html}
+    return {"repo": full_name, "columns": payload}
+
+
 def _card_ages(
     full_name: str, open_issues: list[dict], board: dict[str, list[dict]]
 ) -> dict[int, dict]:
@@ -1052,6 +1123,7 @@ async def _do_capture(
         repo_full_name, issue["number"], "created",
         to_column=column, source="capture",
     )
+    await _publish_board_changed(repo_full_name)
     return {
         "number": issue["number"],
         "title": issue.get("title", title),
@@ -1500,6 +1572,7 @@ async def api_move(
                 "Label sync failed for %s#%s: %s", repo_full_name, issue_number, exc
             )
             result["label_sync"] = "failed"
+    await _publish_board_changed(repo_full_name)
     return result
 
 
@@ -1534,6 +1607,7 @@ async def api_create_issue(
     issue = await gitea.create_issue(owner, repo, title, body)
     move_issue(repo_full_name, issue["number"], column)
     log_event(repo_full_name, issue["number"], "created", to_column=column)
+    await _publish_board_changed(repo_full_name)
     return JSONResponse(
         {
             "ok": True,
@@ -1736,6 +1810,7 @@ async def api_toggle_issue_label(
         await gitea.add_issue_label(owner, repo, number, label_id)
     else:
         await gitea.remove_issue_label(owner, repo, number, label_id)
+    await _publish_board_changed(f"{owner}/{repo}")
     issue = await gitea.get_issue(owner, repo, number)
     return {
         "ok": True,