Background: The integration of generative artificial intelligence (GenAI) in workplaces, especially in knowledge-intensive environments such as consulting, ICT, and business services, creates new skill requirements that are not sufficiently addressed by existing frameworks such as DigComp. Although DigComp remains a key reference for European digital skills policy, it does not fully explain how GenAI-related competences are mobilised through HRM practices or how they influence inclusion and performance. This study introduces two novel constructs: Prompt Self-Efficacy (PSE), describing employees’ confidence in designing effective prompts for GenAI tools, and GenAI Readiness (GAIR), referring to their preparedness to integrate such tools into daily work. These constructs aim to capture emerging competences not covered by traditional frameworks. Methods: A structured 5-point Likert questionnaire was completed by 420 knowledge workers from Greece and Italy—two Southern European countries with similar work cultures and educational systems, comparable in digital transformation dynamics. Participants were employed in consulting, ICT, and business service sectors, all working in hybrid arrangements that combine on-site and remote tasks within the same week. Data were analysed using PLS-SEM, assessing measurement reliability, structural validity, predictive relevance (PLSpredict), and performance priorities (IPMA). Results: Findings confirmed that PSE positively predicts GAIR, while both GAIR and Inclusive e-HRM practices enhance Perceived Skill Utilisation (PSU). PSU acts as the key mechanism linking GenAI competences to digital task performance. Conclusions: The study highlights the limits of DigComp in the GenAI context, proposing HRM-oriented and socially grounded constructs that better explain skill utilisation and performance. It provides HR professionals with a practical priority map for strategic interventions enhancing equality, development, and effectiveness in digital workplaces.