If you didn't SOLI out before 31/12/20 then you no longer have an EASA licence. Some EU states are less "stringent" in issuing EASA licences based on your UK licence, you just have to know which one to choose. If your TRE has both licences then he/she can validate your UK and EASA licence at the same time in one PC as long as the requirements don't drift too far apart which they shouldn't.