Then installing heating loops there is correct and opens up more heated area; the heating engineer is right.
Correct. However, it must also be said correctly that a tub on screed in new construction is complete nonsense (although technically not "wrong"). The load of a full tub + user must always be acoustically decoupled and carried via the raw ceiling. As a rule, neither insulation nor screed is designed for such loads; in this area the screed sinks and all joints crack.
What do unnecessary heating loops have to do with building cheaply, please?
What does the execution plan say about screed, areas to be left open, and slopes in the shower area? Often with "cheap craftsmen," the fee is only enough for a blunt craft implementation of the - however described and recorded in an execution plan - services. Often there is no time/money for thinking, or simply no experience.