Well productivity is just GDP produced per hour per worker. An individual workers can't change productivity significantly. Productivity can only be changed in any significant manner by capital investment. A worker from 150 years ago can never produce as much garments as worker today with the current sowing machines. The sowing machines make the current worker significantly more productive than the one 150 years ago. That sowing machine is the capital investment that makes the modern worker more productive than the old timer. Productivity is different across sectors but that's a sectoral difference which is also unaffected by individual workers. A Tim Hortons worker would always be less productive than a plumber or a machinist, regardless of who a particular Tim Hortons worker is.

An immigrant Tim Hortons worker bringing their elderly parents would put extra strain on OAS but it wouldn't have any material difference on Tim Hortons wages if the have the exact same workers' rights as a Canadian, would it?

A key point here is that the economy doesn't stay static when new people enter the workforce. Whether it's Canadian kids or immigrants, new entrants present both extra labour as well as extra demand for goods. As long as there's natural resources to produce the extra goods demanded by the new entrants and labour to transform those natural resources into the goods demanded, the economy expands. That's literally how the economy grows - more hands turn more natural resources into more physical things.