{# Method-picker Alpine component (S-120). Mounted once at the Studio page level (see ``studio.html``). Listens for ``studio:open-method-picker`` window events dispatched by the column method pill (rendered in ``spec_row.html``) and renders a modal showing the catalogue methods that apply to the column's dtype. Event payload: {table, column, method, provider, dtype} Behaviour: * On open: fetches ``/api/generators?dtype=`` once (or the full catalogue when dtype is unknown), groups by provider, renders buttons. The currently-selected ``(provider, method)`` is shown highlighted. * On select: ``PUT /api/spec/tables/{t}/columns/{c}`` with ``HX-Request: true`` so the server returns the re-rendered ``spec_row.html`` fragment; the picker swaps the matching ``[data-column="."]`` row in place via outerHTML. * On dismiss: closes the modal; clicking outside content closes too. Failure paths are intentionally non-fatal — fetch errors surface a human-readable line and keep the existing row untouched. #}