refactor: cleanup backend structure

tasks.toml

@@ -4,7 +4,7 @@ run = 'mise dev:tmux'
 ["dev:tmux"]
 description = 'Run BE & FE in tmux'
 run = [
-    'tmux new-window "cd backend; go install; PORT=8912 air"',
+    'tmux new-window "go install; PORT=8912 air"',
     'tmux split-window "cd frontend; bun install; PORT=8913 bun src/index.tsx"',
     'sleep 0.1 && (xdg-open "http://localhost:8913" || open "http://localhost:8913")'
 ]
@@ -16,7 +16,7 @@ run = [
 ]
 
 ["format:backend"]
-run = 'gofmt -w backend/'
+run = 'gofmt -w .'
 
 ["format:frontend"]
 run = 'bun --cwd frontend eslint --fix'