The Data Act covers personal and non-personal data, but it does not supersede the GDPR. Article 1(5) says personal data protection law continues to apply and prevails in the event of conflict.
Article 37(3) gives GDPR supervisory authorities responsibility for monitoring Data Act application insofar as personal data protection is concerned. Article 40 then gives DPAs, within their competence, power to impose GDPR-style administrative fines for infringements of Data Act obligations in Chapters II, III, and V.
In practice, a Data Act enforcement file should mark whether the issue is about access to connected-product data, B2B mandatory data sharing, public-sector access, cloud switching, trade secrets, or personal data protection. Personal data questions such as valid legal basis, data subject access, portability, and classification of personal data may need DPA handling.