The feed_overlap setting was mainly introduced to make it easier to annotate partial streams with multiple annotators, based on what's already present in the dataset and annotated by other people. (Before that, you had to implement a custom stream that kept checking the database, which worked, but was a bit inconvenient.) We later adjusted the feed overlap mechanism a couple of times and it should now behave the same as separate instances, for consistency (in the latest version of Prodigy – although, there may be more changes to the stream mechanism in the future). But it's still not something we'd necessarily recommend because it just adds another layer of abstraction.
(Tbh, I kinda regret shipping or at least documenting this so early – it's an internal API we added for Prodigy Teams and something people wanted to try, so we exposed parts of it. But it turned out to be a lot trickier to use in Prodigy Standalone.)
In this case, you wouldn't need a session name – you'd just have a unique URL instead of the same URL with an added unique session name. Under the hood, the dataset structure would be very similar, too – if you're using multi-user sessions, Prodigy will always create a separate session dataset, e.g. dataset_name-ines.
If you have separate instances, your annotations would be all datasets starting with dataset_name – or you could have your recipe add to dataset_name as well, in which case, the resulting dataset structure would be identical to what you get with multi-user sessions.