North American Nest thermostats need a compatible low-voltage control interface.
Do not connect a North American Nest thermostat directly to a 120 V or 240 V heating circuit. Google specifies compatibility with suitable 24 V systems. Electric floor heating needs an appropriate relay/transformer interface and the required electrical protection.
The WarmlyYours Nest integration drawing shows an RC840T relay/transformer matched to the heater voltage, with low-voltage R, C and W control connections. Follow the diagram for the actual Nest generation and heating layout. The interface does not add a floor-temperature sensor input to Nest, so it must not remove temperature protection required by the flooring or heating assembly.
Use Google’s compatibility checker for the exact Nest model and terminal functions. Heating/cooling stages and accessory support vary by generation. A C wire or Nest Power Connector may be required; do not rely on the old claim that a C wire is needed only rarely.
Have a qualified installer verify the complete system before replacing an existing line-voltage floor-heating thermostat.
Sources: Google Nest compatibility guidance and WarmlyYours Nest integration diagram.