fix(api): change auth status routes from GET to POST

- /auth/github/status, /auth/codex/status, /auth/claude/status use POST
- WHY: status requests carry a body (envGlobalPath, claudeAuthPath)
- INVARIANT: all 3 auth status endpoints match CLI apiPost() calls

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: skulidropek

packages/api/src/http.ts

@@ -450,7 +450,7 @@ export const makeRouter = () => {
         return yield* _(jsonResponse(result, 200))
       }).pipe(Effect.catchAll(errorResponse))
     ),
-    HttpRouter.get(
+    HttpRouter.post(
       "/auth/github/status",
       Effect.gen(function*(_) {
         const req = yield* _(HttpServerRequest.schemaBodyJson(AuthGithubStatusRequestSchema))
@@ -474,7 +474,7 @@ export const makeRouter = () => {
         return yield* _(jsonResponse(result, 200))
       }).pipe(Effect.catchAll(errorResponse))
     ),
-    HttpRouter.get(
+    HttpRouter.post(
       "/auth/codex/status",
       Effect.gen(function*(_) {
         const req = yield* _(HttpServerRequest.schemaBodyJson(AuthCodexStatusRequestSchema))
@@ -498,7 +498,7 @@ export const makeRouter = () => {
         return yield* _(jsonResponse(result, 200))
       }).pipe(Effect.catchAll(errorResponse))
     ),
-    HttpRouter.get(
+    HttpRouter.post(
       "/auth/claude/status",
       Effect.gen(function*(_) {
         const req = yield* _(HttpServerRequest.schemaBodyJson(AuthClaudeStatusRequestSchema))