According to #dgcnect this page will track all EDICs set up by MS through implementing decisions by the EC. They also said every EDIC is expected to have their own website with contact details and composition. So no company register style set-up with UBO type info.

https://web.archive.org/web/20230507142920/https://ec.europa.eu/commission/presscorner/detail/en/qanda_21_4631

EC Q&A on EDICs

European digital infrastructure consortia are as of #2022/12/14 a new legal entity. Decision (EU) 2022/2481 of 14 December 2022 establishing the Digital Decade Policy Programme 2030

Requirement is that Member States may implement a multi-country project by means of an EDIC. The EC will than create them as legal entity by the act of an EC decision on the consortium funding. There is a public register for them.

No mention of UBO (although if members are publshed, those members will have UBO registered).