The 72% figure comes from the survey question 'same-sex marriage should be allowed throughout Europe' in Special Eurobarometer 535 (fieldwork April–May 2023, published December 2023), which is the most recent dedicated EU-wide survey found for this indicator; no newer EU-wide figure was located in this search.
The second part of the original statement ('64% believe in trans rights') was not independently verified within the search limits; only the same-sex marriage figure (72%) is confirmed here.
The figure reflects opinion at the time of fieldwork (2023), roughly three years before the speech; support could have shifted since.
SecondaryILGA-Europe72% of respondents say that same sex marriage should be allowed throughout Europe; up three pp's since 2019.
SecondaryEquinet Europe (European Network of Equality Bodies)72% of respondents think that same-sex marriage should be allowed throughout Europe. ... Eurobarometer 535 April-May 2023 Discrimination in the European Union.