Mirrors the architecture established by the web (#25182), browser
(#25214), and video_gen (#25126) plugin migrations:

* `tools/fal_common.py` — stateless atoms shared by both FAL-backed
  plugins (image_gen + video_gen). Holds the lazy `fal_client` import
  helper, `_ManagedFalSyncClient`, `_normalize_fal_queue_url_format`,
  `_extract_http_status`. Stateful pieces (`fal_client` module global,
  `_managed_fal_client*` cache, `_submit_fal_request`,
  `_resolve_managed_fal_gateway`, `_get_managed_fal_client`)
  intentionally stay on `tools.image_generation_tool` so the existing
  `monkeypatch.setattr(image_tool, ...)` patch sites keep working
  unchanged.

* `plugins/video_gen/fal/__init__.py` — drops its inline
  `_load_fal_client` duplicate; consumes `tools.fal_common.import_fal_client`.

* `plugins/image_gen/fal/{plugin.yaml,__init__.py}` — new plugin.
  `FalImageGenProvider` is a thin registration adapter that resolves
  the legacy module via `import tools.image_generation_tool as _it`
  and calls `_it.image_generate_tool` + `_it._resolve_fal_model` at
  call time. The 18-model catalog, `_build_fal_payload`, managed-
  gateway selection, and Clarity Upscaler chaining all remain in
  `tools.image_generation_tool` as the single source of truth —
  the plugin is a registration adapter, not a parallel implementation.

* `tools/image_generation_tool.py::_dispatch_to_plugin_provider` —
  drops the `configured == "fal"` skip. Setting `image_gen.provider:
  fal` now routes through the registry like any other provider; the
  plugin re-enters this module's pipeline so behavior is identical.
  Unset `image_gen.provider` still falls through to the in-tree
  pipeline (preserves no-config-with-FAL_KEY UX from #15696).

* `hermes_cli/tools_config.py` — drops the hardcoded "FAL.ai" row from
  `TOOL_CATEGORIES["image_gen"]["providers"]` (now injected by
  `_plugin_image_gen_providers` like every other backend) and the
  `getattr(provider, "name") == "fal"` skip that protected against
  duplication with the hardcoded row. The "Nous Subscription" row
  stays as a setup-flow entry — same shape browser kept "Nous
  Subscription (Browser Use cloud)" after #25214.

* `tests/plugins/image_gen/test_fal_provider.py` — 14 cases covering
  the ABC surface, call-time indirection (verifying
  `monkeypatch.setattr(image_tool, "image_generate_tool", ...)` takes
  effect through the plugin), response-shape stamping, exception
  handling, and registry wiring.

* `tests/plugins/image_gen/check_parity_vs_main.py` — subprocess
  harness mirroring `tests/plugins/browser/check_parity_vs_main.py`.
  Pins one path to origin/main, one to the worktree; runs six
  scenarios (unset, explicit-fal-no-creds, explicit-fal-with-creds,
  explicit-fal-with-model, typo provider, managed-gateway-only) and
  diffs the reduced shape `{dispatch_kind, provider_name, model}`
  per scenario. The only acceptable diff is "legacy_fal → plugin
  (fal)" for explicit-FAL paths — every other delta is flagged as
  a regression.

* `tests/hermes_cli/test_image_gen_picker.py::test_fal_surfaced_alongside_other_plugins`
  — flips the previous `test_fal_skipped_to_avoid_duplicate` to
  match the new shape (FAL is a plugin now, no dedup needed).

Verified: 195/195 tests across
`tests/{tools/test_image_generation*,tools/test_managed_media_gateways,plugins/image_gen,plugins/video_gen,hermes_cli/test_image_gen_picker}.py`
pass on this branch with no test patches modified outside the picker
test that asserted the old skip behaviour.

Fixes #26241