What type of underlayment should be used when installing engineered wood over underfloor heating
I don't know why you would've been advised to glue or lock a floating floor down. This a very bad idea &amp; could make the floor cup or ridge if the floor can't move. Parquet is very different in being extremely small pieces with extremely small omnidirectional movement in a whole lot of very small areas.

Having no underlayment is the typical way &amp; allows any moisture from condensation to escape, radiant floor's secondary activity. Foremost, is abiding by the Flooring Manufacturer's written instructions &amp; approvals (over the phone means nothing) above &amp; beyond whatever I or anyone else tells you. Do what the Warrantor says &amp; even file pictures away to back up your by-the-book professional installation.