In a large bowl, combine ground beef, rice, minced onion, garlic, egg, cumin, oregano, salt, and pepper. Mix gently until just combined. Roll into 1-inch balls.

For Instant Pot: Select sauté function and brown meatballs in batches for 2-3 minutes per batch. Remove and set aside.

In the same pot, sauté carrots, celery, and onion for 2-3 minutes. Add garlic and cook 30 seconds more.

Deglaze pot with broth, scraping up browned bits. Add remaining beef broth, canned tomatoes, and bring to simmer.

For Instant Pot: Return meatballs to pot. Seal lid and cook on high pressure for 8 minutes. Quick release, add zucchini, cook 3 more minutes on high pressure. Quick release again.

For Slow Cooker: Transfer meatballs, vegetables, broth, and tomatoes to slow cooker. Cook on low 6-7 hours or high 3-4 hours. Add zucchini during last 30 minutes.

Stir in fresh cilantro and lime juice. Taste and adjust seasoning as needed.

Serve hot, garnished with additional cilantro and lime wedges.