There are three broad Ultra Ultra 2 categories, for support of pulse oximetry / blood oxygenation: those US models with a model number ending in LL/A, those US models ending in LW/A, and those from the rest of the world and ending in other model suffixes.
Those models ending in LL/A and the models from the rest of the world have pulse oximetry support. Those models ending with LW/A can only display that pulse oximetry data via a paired iPhone.
Identify your Apple Watch - Apple Support
Pulse rate display is available everywhere.
ECG display is available (most) everywhere, but is only available for people 22 years and older.
To conserve power, Watch goes to some effort to avoid using cellular communications functions, absent a requirement. Where possible, Watch uses the iPhone for its hardware capabilities and greater battery capacity.
With a paired iPhone, an eSIM and a cellular plan is irrelevant for any case where the Watch is within range of the paired iPhone, or where the Watch has access to a known Wi-Fi network.
Watch will be unable to connect and communicate when out of range of the paired iPhone or of a known Wi-Fi, if no cellular plan is available.