Which exact *G privilege are you inquiring about? They are listed here: https://www.staralliance.com/en/benefits-and-privileges

There is no such thing as "*G carry-on privilege" -- that is always airline specific/dependent. However, any status (25K and up) with AirCanada will confer free carry-on in Economy-Basic. Actually, it doesn't say that anywhere I can find.. so even a Super-Elite is probably not permitted carry-on in Economy-Basic now.

Airlines around the world have different carry-on allowances and sizes, and each has their own rules about it all.