Pinning is of course part of the elegant solution. There are some great videos about it:
In practice, it's probably not going to matter all that much because the average web service does way more time-expensive things like disk IO or SQL queries. The more significant effect is that async-await being really really fast enables you to use it in more places. For example, if you have a tight computation loop where different aspects of the logic are meshed together in a hard-to-read way, now you could try detangling it into several async actors talking to each other to make it more readable, without utterly destroying the performance characteristics.
But those are rather just thread-safety annotations and not a memory-model