fix(doctor): oMoMoMoMo branding, remove providers check, fix comment-checker detection

Rename header to oMoMoMoMo Doctor to match installation guide branding.
Remove providers check entirely — no longer meaningful for diagnostics.
Fix comment-checker detection by resolving @code-yeongyu/comment-checker package path
in addition to PATH lookup.

src/cli/doctor/checks/index.ts

@@ -2,13 +2,12 @@ import type { CheckDefinition } from "../types"
 import { CHECK_IDS, CHECK_NAMES } from "../constants"
 import { checkSystem, gatherSystemInfo } from "./system"
 import { checkConfig } from "./config"
-import { checkProviders, gatherProviderStatuses } from "./providers"
 import { checkTools, gatherToolsSummary } from "./tools"
 import { checkModels } from "./model-resolution"
 
 export type { CheckDefinition }
 export * from "./model-resolution-types"
-export { gatherSystemInfo, gatherProviderStatuses, gatherToolsSummary }
+export { gatherSystemInfo, gatherToolsSummary }
 
 export function getAllCheckDefinitions(): CheckDefinition[] {
   return [
@@ -23,11 +22,6 @@ export function getAllCheckDefinitions(): CheckDefinition[] {
       name: CHECK_NAMES[CHECK_IDS.CONFIG],
       check: checkConfig,
     },
-    {
-      id: CHECK_IDS.PROVIDERS,
-      name: CHECK_NAMES[CHECK_IDS.PROVIDERS],
-      check: checkProviders,
-    },
     {
       id: CHECK_IDS.TOOLS,
       name: CHECK_NAMES[CHECK_IDS.TOOLS],