The "Mycenaean like" E-V13 samples were the EIA invaders from the Danube and Northwards. Many years ago there was an E sample from Svilengrad with Southern profile, alongside Bulgarian LBA sample which was more Northern. back in the day authors speculated that two different groups lived in Thrace, and even segregated, with E sample representing local EEF's.
Now they tested again Svilengrad and another nearby site and again the result was the same. But these people were not locals, this culture was an "invader". There are many Neolithic Bulgarian and EBA samples, none are E. Neolithic E wasn't found in Bulgaria, but in W.Balkans, Pannonia, Carpathians, C.Europe, Spain.. LIA , other IA and LA samples from Bulgaria show this is how Thracians looked like. Also one R-Z93 was found alongside.
The upcoming Hungarian study contains two E-L539 samples from East and Northeastern Hungary. They are practically certain to be V13 (they used on diagram 10k-15k old SNP's except for the R1b). E samples from Carpathian basin are from EBA and LBA. They do carry substantial Steppe ancestry, much higher than Bulgarian E samples. EBA almost 40 % and LBA sample almost 50 %.
But as this study shows, NE Hungary was also populated by various Minoan like peoples, often carrying J2a. Also the majority of invading Tumulus culture R1b's were very Southern shifted. This must have influenced the formation of Thracian autosomal profile as it was.
Bottom line There is no E on the Balkans in BA, there is Steppe heavy E in Carpathians in BA. The culture where Bulgarian samples are from is a direct descendant of the culture where Steppe heavy LBA E sample is from.
So there is nothing to debate, unless those E-L539 are somehow E-V12 or E-V22 which they won't be. Originally E-V13 was more Steppe derived in auDNA, prior to their invasion of the Balkans between LBA and EIA their autosomal profile was significantly altered by Carpathian locals. This Southern profile invaded, caused Southern autosomal shift and brought the Thracian language to Bulgaria in EIA.
These results also point towards E being IE-zed in EBA, as there seems to be auDNA continuity from EBA to LBA. And their root is not the Steppe, but might be an area very near to the Steppe. Possibly some R1a will also be found alongside EBA E sample.