Please see this guide: Link
By flashing mbn file, you can access full functionalities your carrier provided (except Rogers, fido, chatr, cityfone). However, due to band differences, please don't expect full speed 5G internet in Canada on this phone. From my test, Rogers 5G is slower than its LTE on my BC72 (it's not the internet issue because I tested on an iPhone).
I checked online about the band information for the US version of Xperia 1 iii, all the 5G bands in Canada are supported so technically you can have a better experience than me.