What is the recommended approach for upgrading a v1 flow that uses the v1 prefect client to create another flow run? The goal is to get both the parent flow and the child flow onto v2. Is it better to upgrade them both at approximately the same time, and use the v2 prefect client to create the child flow? Or is it better to switch to using the v1 graphql API (without the prefect client) to create the child flow run, then upgrade the parent flow, then upgrade the child flow, and finally upgrade the parent flow to use either the v2 prefect client or the REST API?

It seems easiest to do them both at once, but you could upgrade the parent before the child if you want to use GraphQL

By any chance is the prefect v2 client capable of creating v1 flow runs?

No, sorry.