Sounds like a good question for FAA, EAA or AOPA but I agree it should count towards "Total Time" since it is a registered aircraft!
Special Light-Sport Aircraft (SLSA) Make/Model Directory
https://www.faa.gov/aircraft/gen_av/light_sport/
It lists the Czeck Sportcruiser.
I personally would get the LSA license at the 20 hour point then go for a Private Pilot license then the LSA CFI at 150 hours. Sounds like a great way to build total flight time! Just my two cents!
From my understanding, once one is an LSA pilot the aircraft categories are additional logbook endorsements ie: LSA airplane, LSA glider, etc.....but not an expert in Light Sport. Recommend EAA or AOPA as a good source of info!
https://www.aopa.org/advocacy/advoca...ut-sport-pilot