Catalog UI shutdown installs the ui extension from the network to call stop_ui_server() #336

What happens

serve_catalog_ui sets server_started = True immediately after _start_duckdb_ui_server
returns (src/hflow/catalog_ui.py:132-133), and shutdown calls stop_ui_server() on that flag
alone (catalog_ui.py:90-95):

def _stop_duckdb_ui_server(catalog_connection, server_started) -> None:
    try:
        if server_started:
            catalog_connection.execute("CALL stop_ui_server()")

stop_ui_server() is a function the ui extension provides. Calling it on a connection that
never loaded the extension makes DuckDB go and install ui from the network, at shutdown,
to run a no-op: there is no server to stop if the extension was never loaded.

Why it is reachable, and where it bites

tests/test_catalog_ui.py:49 replaces the real starter:

monkeypatch.setattr(catalog_ui, "_start_duckdb_ui_server", record_server_start)

The stub records the call and returns. It never runs INSTALL ui / LOAD ui, but
serve_catalog_ui still sets server_started = True, so every one of these tests reaches
CALL stop_ui_server() with no extension loaded and DuckDB fetches the extension over the
network while the test is tearing down.

That is almost certainly the test_catalog_ui timing flake three separate contributors reported
on 2026-08-31 (#326, #327, #328), all describing a thread-shutdown or timing failure that passed
on a rerun. A network fetch inside a teardown that a test is waiting on with a fixed timeout is
exactly that shape, and it makes the suite depend on network access it otherwise does not need.

What to build

Only call stop_ui_server() when the ui extension is actually loaded on that connection:

def _ui_extension_is_loaded(catalog_connection) -> bool:
    row = catalog_connection.execute(
        "SELECT count(*) FROM duckdb_extensions() WHERE extension_name = 'ui' AND loaded"
    ).fetchone()
    return row is not None and int(row[0]) > 0

and gate the call on server_started and _ui_extension_is_loaded(...).

Definition of done

1. Shutdown does not call stop_ui_server() when the ui extension is not loaded.
2. A real UI session still stops its server on shutdown.
3. A test pins that the stubbed-starter path issues no stop_ui_server() call. Recording the
   statements executed on the connection is enough; asserting DuckDB's install behavior is not
   the point.
4. Existing catalog UI startup, port-conflict, and refresh behavior is unchanged.

Validation

uv sync --locked --all-extras
uv run ruff check --fix
uv run ruff format
uv run ty check
uv run pytest -q

Run plain uv run pytest -q from the repo root.

Notes

Found by @rakesh0x while working on #291. The fix is written and validated already, it just
needs to travel separately from an examples change.