Add typed settings areas to the REST API

/api/v1/settings/router/firewall, .../router/lans/<name>, .../system, down to
a single option: GET reads, PUT replaces, PATCH merges, DELETE removes, with
the settings' ETag/If-Match and the same limits as the whole-document edit
(editSettings is now shared). Values are checked against a JSON Schema made
from the option documentation (schema.go reads the types, which nixosOptionsDoc
describes in words); a wrong type, a value out of range or an unknown key is
refused with its place. The OpenAPI document has the area paths with their
schemas; the API reference page lists every area's options.

Tests: unit tests for the type reader, the validator and the paths; the real
option file and a router's own settings validate (ROUTER_OPTIONS_JSON,
LIVE_SETTINGS_JSON); a subtest in apply.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01AeFqV9dZrK6nipHkPfyM4F

pkgs/router-webui/main.go

@@ -221,7 +221,9 @@ type app struct {
 
 	tokens      *tokenStore
 	settingsMu  sync.Mutex // edits through the API read, patch and write the settings file
-	optionsFile string     // JSON documentation of the router options, for the MCP resource ("" if none)
+	schemaOnce  sync.Once
+	schemaVal   map[string]any // the settings schema, from optionsFile (nil if none)
+	optionsFile string         // JSON documentation of the router options, for the MCP resource ("" if none)
 }
 
 func withOptions(a *app, file string) *app {