It's not the same though. You need a true queue here. Just seeing if there is already something in flight does not do it, because maybe the new task was triggered due to a push from the server or something, indicating that new data was available, while the existing (running) task is already half way through and didn't get that data.
It seems what we are supposed to use is a AsyncStream (How do you use AsyncStream to make Task execution deterministic?). It just seems like a very heavy handed approach. I feel like this is such a common pattern, and no doubt cause of many bugs, that making at simple as possible to avoid, with a simple keyword, would help a lot.
You basically want to have each actor have an AsyncStream internally, with atomic funcs being submitted in a single parent Task. Something like that.