The RCHT9610WFSW2003/U bundle includes one Smart Room Sensor and a C-wire adapter. Those parts matter when comparing listings: a thermostat-only or multi-sensor package is a different purchase. The exact kit identity is a more useful starting point than a photo that merely shows a T9 thermostat.
T9 compatibility depends on the heating/cooling arrangement, stage count and power wiring. Its published limits include supported 24 VAC systems; the installation instructions exclude 120–240 V baseboard and millivolt systems. Check the manufacturer’s complete requirements for the actual equipment before treating an included adapter as the solution.
A room sensor can influence a shared temperature target, but the thermostat does not independently condition each room. It is a sensible comparison with ecobee when room selection is the decision you want to improve. A room that remains uncomfortable because of air delivery or insulation may need work beyond a thermostat change.