Xperia 10 III works fairly well in the USA on T-Mobile with SFOS, but not perfectly. only some of the LTE bands are supported, and not the most common one. (Xperia 10 V may even support 5G on T-Mobile in some places)
if the C2 has the 4G bands supported by T-Mobile, it will probably work.
however, it is unlikely that it will have those bands, since those bands are more or less only used in the USA.