What approval would have covered
Converting a garage into living space engages building regulations across six headings at once: structural adequacy, because garage foundations and walls are not built to carry a habitable room; fire safety and escape; ventilation and moisture; thermal insulation to floor, walls and roof; sound insulation; and electrical work, which has to be done by someone qualified to certify it.
A completion certificate is the single document that says all of that was checked. Its absence does not prove anything is wrong. It means nobody independent confirmed that anything is right.