Enforcement sits with the national supervisory authorities. One of the best known fines came from the French regulator: 50 million euro for Google, because information about data processing was spread too thin and consent for personalised advertising was not validly obtained.
In 2022 the Austrian, French and Italian authorities each ruled that using Google Analytics breached the GDPR, because personal data flowed to the United States without an adequate level of protection. In July 2023 the European Commission adopted the EU-US Data Privacy Framework, which restores a legal basis for transfers to certified US companies. That takes the sharpest edge off those rulings, but the matter isn't settled: the two frameworks that preceded it were both struck down by the Court of Justice.