I did install fiddler, but it didn't shed any light on what exactly is happening.

Allow me to summarize the request to "Click the Auto-complete button on the Baseline tab and select "Latest Released" but then fully automated. And you want LatestReleased on any baseline entry, so in turn it means you want to truncate your existing baseline and start from scratch, navigating the map-submap-tree-structure always selecting the LatestReleased version.

Before we tried to get you going by passing the right object identifiers, etc. The hint towards Publication Manager was illustrate that it can be done, although I must admit here that Publication Manager handles more use cases: Conflict resolving like your overwrite everything, so Publication Manager does more than a one-stop big calculate-save operation. But recursively does reports, in turn asking user confirmation where required, and updating the client-side Baseline tab with information... only upon Save the actual action is saved in the repository. So Fiddler shows something more complicated than required.

So indeed you don't want to complete-the-existing-baseline, you actually want to generate a new baseline from scratch. Instead of CompleteBaselineByCandidateAndMode, can you have a look at CompleteReportByCandidateAndMode where you don't provide an existing baseline as starting point (read: no existing versions of topics). You provide an empty starting baseline report (again: no existing versions, like start from root map v2 or something). Keeping psExtendBaselineId empty as well.

Please verify if this is the result you are looking for. In turn, it is still a report as result which needs to be converted to an Update to actually save it. 

I did not have the time to write the code, so this is a theoretical approach to get this question on the rails again. That takes quite some time to work out.

Indeed, CompleteReportByCandidateAndMode does seem to do what I want it to do when I pass an empty baseline. I've taken that report and used it to update the existing baseline successfully (I think).

In the baseline update API call, what  does "source = expand:LatestReleased" do? There are several options to choose from, but I'm not sure what this field does.

Also, is there any drawback to updating the existing baseline vs starting a new one?

Thanks!

Nice of you to share that you got further!

The "source" is mostly a field to indicate if the version selection in Publication Manager happened explicitly by the user, or was the result of an automated action (like an Autocomplete LatestReleased which makes the most sense for your scenario - other values are on SDL Documentation). It are mostly statistics, and have no effect downstream. 

If you create a new baseline you need to assign it to your publication version (or if you are sharing your baseline across multiple publications). There is hardly any difference, the new baseline holds exactly what you wanted (probably ;-)), while the reuse will merge with what users already did. If it was up to me, I think the merge makes more sense as publications and their content (maps, submaps, topics, images, etc) are an ever moving target until it reaches some kind of deadline.

-Dave