Provided you are prepared to work on it at different times, I’d say save the project to either a local NAS or cloud and you can both open it at different times, making certain to close out of the project when you’re finished. (Set Scrivener to close after a couple of minutes of inactivity)
That prevents you having to transfer work back and forth and the potential for getting things out of sync.
That is not entirely true, in the broadest sense, though it is technically true. What is fact is that you cannot both be working on the same data at the same time—whether that be on the same disk, or two different disks with an intermediate technology making those two disks act as one (like Dropbox). So everything you’ve heard there is right.
What it sounds like you haven’t heard is that it is entirely possible for two people to be working on the same project simultaneously. We aren’t talking about data here, we’re talking about something more abstract, something more akin to how Github works (for those that know what that means). In such a system, one provides their colleague with a copy of the data, which they can then go off and work on at their own pace. Later on they return their copy to you, and you merge it back into your copy of the data. You then give them another copy based on the updated merged project that contains both of your concurrent edits, and repeat.
It’s pretty easy to do, and provides the most freedom as you don’t have to worry about who is working when. There are still some common sense things to consider, like avoiding the same exact areas within the project. If you both edit the same subsection then when it comes time to merge, the software will have to split the work into another binder item since there will be no clear answer as to which is best. You’ll then have to go review the two versions and probably manually merge them yourself with cut and paste. Not the end of the world, but the sort of thing better avoided through some form of communication (like using colour Labels to indicate what items you have “checked out” for work).
Read more about it in the above post, along with a lot of good discussion on this topic, above. You should find that the convenience tools Scrivener has for using this workflow clear up a lot of ambiguity, like what you point out about knowing what “the latest version is”. If the copies you share with each other are all stacked into one folder, and every copy is neatly date and timestamped automatically, it’s pretty difficult to get the answer to that question wrong without any process at all. But process, the stuff we do inside the project to communicate with each other, always helps. A note at the top of the binder that you both add to, jotting down briefly what you’ve done recently, is an easy way to keep each other up to date, and to help flag cases where you realise you’ve accidentally opened yesterday’s copy because your notes are gone.