For API edits to create or update claims, the input syntax varies based on the data type of the property being used. The number of example(s) in the documentation are small, and do not cover all cases.
For example, https://www.wikidata.org/w/api.php?action=help&modules=wbsetclaimvalue has a single example, which will only show you how to add an Item type claim, but this approach will not work for adding strings. https://www.wikidata.org/w/api.php?action=help&modules=wbcreateclaim has 4 examples, but still wouldn't help you to post a monolingual text claim like P1476 ("title"), for which you need to know that you put in a dict with a language code. And so on.
For most of these, if you are willing to dig, you can intuit the correct inputs from looking at the data structure in JSON for existing items, but this should presumably actually be documented somewhere in full for usability.