The logical business flow
Few people love process diagrams but when you really need them and none exists, you might be in a world of doo-doo.
You could certainly go full-bore with EventStorming and essentially encapsulate the business flows there.
An optional approach could be to do some (lightweight?) BPMN model, though I would perhaps rather lean back into the full EventStorming approach in that case so we aren't caught in unnecessary complexity spreading around the work.
Already at the start, if possible, it's wise to have some visual and logical model to describe what's going on. This type of flowchart may in complex cases become unwieldy and cumbersome.
Here we see a state chart that represents the key flow, color-coded into the various state it may take. In this case, we are significantly improving the understanding of what a technical implementation would represent.
The diagram as presented here has been modified several times to fit the logical model.