When importing a phone, you'll need to make sure it'll first work with the frequencies that Telus uses. For LTE, it should work fine in most urban areas. It will not get LTE in some rural areas.
The Xperia 1 iii coming from Asia will not work in Canada on 5G. It does not support both of the 5G frequencies in use here. 5G on band n78 might work but that frequency band isn't that common to find yet. The Asian version of the Xperia 1 iii doesn't support 5G band n66, which is by far the most common frequency used in Canada. There is no unlock to fix the supported frequencies. Only option would be to order the US model of the Xperia 1 iii instead since their network frequencies and Canada's are mostly the same.
A lot of imported phones also don't seem to get VoLTE or wifi calling working even if the phone supports it.