fix(tsukihime): finish rename outside src and harden API base URL

CodeRabbit caught that the rename stopped at src/, leaving the mpv plugin
emitting the old CLI flag.

- plugin/subminer/session_bindings.lua: openTsukihime -> --open-tsukihime
  (the old flag no longer exists, so the overlay shortcut was a no-op)
- docs-site: rename the integration page, nav entry, and shortcuts row;
  rewrite the page for the TsukiHime API rather than find-and-replace
- changes/: rename the changeset and describe TsukiHime
- config.example.jsonc (+ docs-site copy): regenerated from definitions
- settings registry: route tsukihime.* to Integrations with the branded
  TsukiHime label (it was falling through to Advanced)
- tsukihimeFetchJson: apiBaseUrl is user config, so a malformed or
  non-HTTP(S) value now returns a structured error instead of throwing

plugin/subminer/session_bindings.lua

@@ -254,8 +254,8 @@ function M.create(ctx)
 			return { "--open-runtime-options" }
 		elseif action_id == "openJimaku" then
 			return { "--open-jimaku" }
-		elseif action_id == "openAnimetosho" then
-			return { "--open-animetosho" }
+		elseif action_id == "openTsukihime" then
+			return { "--open-tsukihime" }
 		elseif action_id == "openYoutubePicker" then
 			return { "--open-youtube-picker" }
 		elseif action_id == "openSessionHelp" then