chore(makefile): rename backend targets to api

- rename Makefile variables and targets from backend to api for naming consistency.
- update dev command messages and reset setup restart flow to use api terminology.

makefile

 WEB_DIR = ./web/default
 WEB_CLASSIC_DIR = ./web/classic
-BACKEND_DIR = .
+API_DIR = .
 DEV_WEB_DEFAULT_PORT ?= 5173
 DEV_WEB_CLASSIC_PORT ?= 5174
 DEV_COMPOSE_FILE = docker-compose.dev.yml
 DEV_POSTGRES_SERVICE = postgres
-DEV_BACKEND_SERVICE = new-api
+DEV_API_SERVICE = new-api
 DEV_POSTGRES_DB = new-api
 DEV_POSTGRES_USER = root
 DEV_SQLITE_PATH ?= one-api.db
 
-.PHONY: all build-web build-web-classic build-all-web start-backend dev dev-api dev-api-rebuild dev-web dev-web-classic reset-setup
+.PHONY: all build-web build-web-classic build-all-web start-api dev dev-api dev-api-rebuild dev-web dev-web-classic reset-setup
 
-all: build-all-web start-backend
+all: build-all-web start-api
 
 build-web:
 	@echo "Building default web..."
@@ -26,17 +26,17 @@ build-web-classic:
 
 build-all-web: build-web build-web-classic
 
-start-backend:
-	@echo "Starting backend dev server..."
-	@cd $(BACKEND_DIR) && go run main.go &
+start-api:
+	@echo "Starting api dev server..."
+	@cd $(API_DIR) && go run main.go &
 
 dev-api:
-	@echo "Starting backend services (docker)..."
+	@echo "Starting api services (docker)..."
 	@docker compose -f $(DEV_COMPOSE_FILE) up -d
 
 dev-api-rebuild:
-	@echo "Rebuilding and starting backend service (docker)..."
-	@docker compose -f $(DEV_COMPOSE_FILE) up -d --build $(DEV_BACKEND_SERVICE)
+	@echo "Rebuilding and starting api service (docker)..."
+	@docker compose -f $(DEV_COMPOSE_FILE) up -d --build $(DEV_API_SERVICE)
 
 dev-web:
 	@echo "Starting default web dev server..."
@@ -60,15 +60,15 @@ reset-setup:
 			-c 'DELETE FROM setups;' \
 			-c 'DELETE FROM users WHERE role = 100;' \
 			-c "DELETE FROM options WHERE key IN ('SelfUseModeEnabled', 'DemoSiteEnabled');"; \
-		echo "Restarting docker dev backend so setup status is recalculated..."; \
-		docker compose -f $(DEV_COMPOSE_FILE) restart $(DEV_BACKEND_SERVICE); \
+		echo "Restarting docker dev api so setup status is recalculated..."; \
+		docker compose -f $(DEV_COMPOSE_FILE) restart $(DEV_API_SERVICE); \
 	elif db_path="$${SQLITE_PATH:-$(DEV_SQLITE_PATH)}"; db_path="$${db_path%%\?*}"; [ -f "$$db_path" ]; then \
 		db_path="$${SQLITE_PATH:-$(DEV_SQLITE_PATH)}"; \
 		db_path="$${db_path%%\?*}"; \
 		echo "Detected local SQLite database: $$db_path"; \
 		sqlite3 "$$db_path" \
 			"DELETE FROM setups; DELETE FROM users WHERE role = 100; DELETE FROM options WHERE key IN ('SelfUseModeEnabled', 'DemoSiteEnabled');"; \
-		echo "SQLite setup state reset. Restart the local backend process before testing the setup wizard."; \
+		echo "SQLite setup state reset. Restart the local api process before testing the setup wizard."; \
 	else \
 		echo "No running docker dev PostgreSQL or local SQLite database found."; \
 		echo "Start the dev stack with 'make dev-api', or set SQLITE_PATH/DEV_SQLITE_PATH to your local SQLite database."; \